1. CMB Online first
 Elmadani, Y.; Labghail, I.

Cyclicity in Dirichlet spaces
Let $\mu$ be a positive finite Borel measure on the unit circle
and $\mathcal{D}(\mu)$ the associated harmonically weighted Dirichlet
space. In this paper we show that for each closed subset $E$
of the unit circle with zero $c_{\mu}$capacity, there exists
a function $f\in\mathcal{D}(\mu)$ such that $f$ is cyclic (i.e.,
$\{p f: p $ is a polynomial$\}$ is dense in $\mathcal{D}(\mu)$),
$f$ vanishes on $E$, and $f$ is uniformly continuous.
Then we provide a sufficient
condition for a continuous function on the closed unit disk to
be cyclic in $\mathcal{D}(\mu)$.
Keywords:Dirichlettype space, cyclic vector, capacity, strongtype inequality Categories:47B38, 30C85, 30H05 

2. CMB Online first
 Kalvin, Victor; Kokotov, Alexey

Determinant of the Laplacian on tori of constant positive curvature with one conical point
We find an explicit expression for the zetaregularized determinant
of (the Friedrichs extensions) of the Laplacians on a compact
Riemann surface of genus one with conformal metric of curvature
$1$ having a single conical singularity of angle $4\pi$.
Keywords:determinant of Laplacian, moduli space, spectral zetafunction, curvature one, conical point, conical singularity, Riemann surface, compact Riemann surface Categories:47A10, 58J52, 30F45 

3. CMB Online first
 Alam, Ihab Al; Lefèvre, Pascal

Embeddings of MÃ¼ntz Spaces in $L^\infty(\mu)$
In this paper, we discuss the properties of the embedding
operator $i^\Lambda_\mu : M_\Lambda^\infty\hookrightarrow L^\infty(\mu),$
where $\mu$ is a positive Borel measure on $[0,1]$ and $M_{\Lambda}^{\infty}$
is a MÃ¼ntz space. In particular, we compute the essential norm
of this embedding. As a consequence, we recover some results
of
the first author.
We also study the compactness (resp. weak compactness)
and compute the essential norm (resp. generalized essential norm)
of the embedding $i_{\mu_1,\,\mu_2} : L^\infty(\mu_1)\hookrightarrow
L^\infty(\mu_2)$, where $\mu_1$, $\mu_2$ are two positive Borel
measures on $[0,1]$ with $\mu_2$ absolutely continuous with respect
to $\mu_1$.
Keywords:MÃ¼ntz space, embedding, essential norm, compact operator Categories:32C22, 47B33, 30B10 

4. CMB Online first
5. CMB Online first
 Gaál, Marcell

Maps on quantum states in $C^*$algebras preserving von Neumann entropy or Schatten $p$norm of convex combinations
Very recently, Karder and Petek completely described maps on density
matrices (positive semidefinite matrices with unit trace) preserving
certain entropylike convex functionals of any convex combination.
As a result, maps could be characterized which preserve von Neumann
entropy or Schatten $p$norm of any convex combination of quantum
states (whose mathematical representatives are the density matrices).
In this note we consider these latter two problems on the set
of invertible density operators, in a much more general setting,
on the set of positive invertible elements with unit trace in
a $C^{*}$algebra.
Keywords:density operator, entropy, Schatten $p$norm, $C^{*}$algebra, normalized trace, preserver Category:47B49 

6. CMB 2018 (vol 61 pp. 717)
 Bu, Shangquan; Cai, Gang

Periodic Solutions of Second Order Degenerate Differential Equations with Delay in Banach Spaces
We give necessary and sufficient
conditions of the $L^p$wellposedness (resp. $B_{p,q}^s$wellposedness) for the second order degenerate
differential equation with finite delays:
$(Mu)''(t)+Bu'(t)+Au(t)=Gu'_t+Fu_t+f(t),(t\in [0,2\pi])$ with periodic
boundary conditions $(Mu)(0)=(Mu)(2\pi)$, $(Mu)'(0)=(Mu)'(2\pi)$, where
$A, B, M$ are closed linear operators on a complex Banach space $X$ satisfying
$D(A)\cap D(B)\subset D(M)$, $F$ and $G$ are bounded linear operators from
$L^p([2\pi,0];X)$ (resp. $B_{p,q}^s([2\pi,0];X)$) into $X$.
Keywords:second order degenerate differential equation, Fourier multiplier theorem, wellposedness, LebesgueBochner space, Besov space Categories:34G10, 34K30, 43A15, 47D06 

7. CMB 2017 (vol 60 pp. 462)
8. CMB 2017 (vol 60 pp. 536)
9. CMB 2017 (vol 61 pp. 240)
 Bu, Shangquan; Cai, Gang

HÃ¶lder Continuous Solutions of Degenerate Differential Equations with Finite Delay
Using known operatorvalued Fourier multiplier results on vectorvalued
HÃ¶lder continuous function spaces $C^\alpha (\mathbb R; X)$, we completely
characterize the $C^\alpha$wellposedness of the first order
degenerate differential equations with finite delay $(Mu)'(t)
= Au(t) + Fu_t + f(t)$ for $t\in\mathbb R$
by the boundedness of the $(M, F)$resolvent of $A$ under suitable
assumption on the delay operator $F$, where $A, M$ are closed
linear
operators on a Banach space $X$ satisfying $D(A)\cap D(M) \not=\{0\}$,
the delay operator $F$ is a bounded linear operator
from $C([r, 0]; X)$ to $X$ and $r \gt 0$ is fixed.
Keywords:wellposedness, degenerate differential equation, $\dot{C}^\alpha$multiplier, HÃ¶lder continuous function space Categories:34N05, 34G10, 47D06, 47A10, 34K30 

10. CMB 2017 (vol 60 pp. 561)
 Kurdyka, Krzysztof; Paunescu, Laurentiu

Nuij Type Pencils of Hyperbolic Polynomials
Nuij's theorem states that if a polynomial $p\in \mathbb{R}[z]$ is hyperbolic
(i.e. has only real roots) then $p+sp'$ is also hyperbolic for
any
$s\in \mathbb{R}$. We study other perturbations of hyperbolic polynomials
of the form $p_a(z,s): =p(z) +\sum_{k=1}^d a_ks^kp^{(k)}(z)$.
We give a full characterization of those $a= (a_1, \dots,
a_d) \in \mathbb{R}^d$ for which $p_a(z,s)$ is a pencil of hyperbolic
polynomials.
We give also a full characterization of those $a= (a_1, \dots,
a_d) \in \mathbb{R}^d$ for which the associated families $p_a(z,s)$
admit universal determinantal representations. In fact we show
that all these sequences come from special symmetric Toeplitz
matrices.
Keywords:hyperbolic polynomial, stable polynomial, determinantal representa tion, symmetric Toeplitz matrix Categories:15A15, 30C10, 47A56 

11. CMB 2016 (vol 60 pp. 196)
12. CMB 2016 (vol 60 pp. 712)
 Chen, ChungChuan

Disjoint Hypercyclicity and Weighted Translations on Discrete Groups
Let $1\leq p\lt \infty$, and let $G$ be a discrete group. We give
a sufficient and necessary condition
for weighted translation operators on the Lebesgue space $\ell^p(G)$
to be densely disjoint hypercyclic.
The characterization for the dual of a weighted translation to
be densely disjoint hypercyclic is also obtained.
Keywords:disjoint hypercyclicity, topological transitivity, weighted translation, $\ell^p$space Categories:47A16, 47B38, 43A15 

13. CMB 2016 (vol 59 pp. 673)
 Bačák, Miroslav; Kovalev, Leonid V.

Lipschitz Retractions in Hadamard Spaces Via Gradient Flow Semigroups
Let $X(n),$ for $n\in\mathbb{N},$ be the set of all subsets of a metric
space $(X,d)$ of cardinality at most $n.$ The set $X(n)$ equipped
with the Hausdorff metric is called a finite subset space. In
this paper we are concerned with the existence of Lipschitz retractions
$r\colon X(n)\to X(n1)$ for $n\ge2.$ It is known that such retractions
do not exist if $X$ is the onedimensional sphere. On the other
hand L. Kovalev has recently established their existence in case $X$
is a Hilbert space and he also posed a question as to whether
or not such Lipschitz retractions exist for $X$ being a Hadamard
space. In the present paper we answer this question in the positive.
Keywords:finite subset space, gradient flow, Hadamard space, LieTrotterKato formula, Lipschitz retraction Categories:53C23, 47H20, 54E40, 58D07 

14. CMB 2016 (vol 59 pp. 564)
 Li, Boyu

Normal Extensions of Representations of Abelian Semigroups
A commuting family of subnormal operators need
not have a commuting normal extension. We study when a representation
on an abelian semigroup can be extended to a normal representation,
and show that it suffices to extend the set of generators to
commuting normals. We also extend a result due to Athavale to
representations on abelian lattice ordered semigroups.
Keywords:subnormal operator, normal extension, regular dilation, lattice ordered semigroup Categories:47B20, 47A20, 47D03 

15. CMB 2016 (vol 59 pp. 734)
16. CMB 2016 (vol 59 pp. 878)
 Wang, Jianfei

The Carleson Measure Problem Between Analytic Morrey Spaces
The purpose of this paper is to characterize positive measure
$\mu$ on the unit disk such that the analytic
Morrey space $\mathcal{AL}_{p,\eta}$ is boundedly and compactly
embedded to the tent space
$\mathcal{T}_{q,1\frac{q}{p}(1\eta)}^{\infty}(\mu)$ for the
case $1\leq q\leq p\lt \infty$
respectively. As an application, these results are used to
establish the boundedness and compactness of integral operators
and multipliers between analytic Morrey spaces.
Keywords:Morrey space, Carleson measure problem, boundedness, compactness Categories:30H35, 28A12, 47B38, 46E15 

17. CMB 2016 (vol 59 pp. 693)
 Chen, ChungChuan

Recurrence of Cosine Operator Functions on Groups
In this note, we study the recurrence and topologically multiple
recurrence of a sequence of operators on Banach spaces.
In particular, we give a sufficient and necessary condition for
a cosine operator function,
induced by a sequence of operators on the Lebesgue space of a
locally compact group, to be topologically multiply recurrent.
Keywords:topologically multiple recurrence, recurrence, topological transitivity, hypercyclicity, cosine operator function Categories:47A16, 54B20, 43A15 

18. CMB 2016 (vol 59 pp. 585)
 Lin, Minghua

A Determinantal Inequality Involving Partial Traces
Let $\mathbf{A}$ be a density matrix in $\mathbb{M}_m\otimes
\mathbb{M}_n$. Audenaert [J. Math. Phys. 48 (2007) 083507] proved
an inequality for Schatten $p$norms:
\[
1+\\mathbf{A}\_p\ge \\tr_1 \mathbf{A}\_p+\\tr_2 \mathbf{A}\_p,
\]
where $\tr_1, \tr_2$ stand for the first and second partial
trace, respectively. As an analogue of his result, we prove a
determinantal inequality
\[
1+\det \mathbf{A}\ge \det(\tr_1 \mathbf{A})^m+\det(\tr_2 \mathbf{A})^n.
\]
Keywords:determinantal inequality, partial trace, block matrix Categories:47B65, 15A45, 15A60 

19. CMB 2016 (vol 59 pp. 326)
20. CMB 2016 (vol 59 pp. 354)
 Li, ChiKwong; Tsai, MingCheng

Factoring a Quadratic Operator as a Product of Two Positive Contractions
Let $T$ be a quadratic operator on a complex Hilbert space $H$.
We show that $T$ can be written as a product of two positive
contractions if and only if $T$ is of the form
\begin{equation*}
aI \oplus bI \oplus
\begin{pmatrix} aI & P \cr 0 & bI \cr
\end{pmatrix} \quad \text{on} \quad H_1\oplus H_2\oplus (H_3\oplus
H_3)
\end{equation*}
for some $a, b\in [0,1]$ and strictly positive operator $P$ with
$\P\ \le \sqrt{a}  \sqrt{b}\sqrt{(1a)(1b)}.$ Also, we
give a necessary condition for a bounded linear operator $T$
with operator matrix
$
\big(
\begin{smallmatrix} T_1 & T_3
\\ 0 & T_2\cr
\end{smallmatrix}
\big)
$ on $H\oplus K$ that can be written as a product
of two positive contractions.
Keywords:quadratic operator, positive contraction, spectral theorem Categories:47A60, 47A68, 47A63 

21. CMB 2015 (vol 59 pp. 3)
 Alfuraidan, Monther Rashed

The Contraction Principle for Multivalued Mappings on a Modular Metric Space with a Graph
We study the existence of fixed points for contraction multivalued
mappings in modular metric spaces endowed with a graph. The
notion of a modular metric on an arbitrary set and the corresponding
modular spaces, generalizing classical modulars over linear spaces
like Orlicz spaces, were recently introduced. This paper can
be seen as a generalization of Nadler's and Edelstein's fixed
point theorems to modular metric spaces endowed with a graph.
Keywords:fixed point theory, modular metric spaces, multivalued contraction mapping, connected digraph. Categories:47H09, 46B20, 47H10, 47E10 

22. CMB 2015 (vol 58 pp. 402)
 Tikuisis, Aaron Peter; Toms, Andrew

On the Structure of Cuntz Semigroups in (Possibly) Nonunital C*algebras
We examine the ranks of operators in semifinite $\mathrm{C}^*$algebras
as measured by their densely defined lower semicontinuous traces.
We first prove that a unital simple $\mathrm{C}^*$algebra whose
extreme tracial boundary is nonempty and finite contains positive
operators of every possible rank, independent of the property
of strict comparison. We then turn to nonunital simple algebras
and establish criteria that imply that the Cuntz semigroup is
recovered functorially from the Murrayvon Neumann semigroup
and the space of densely defined lower semicontinuous traces.
Finally, we prove that these criteria are satisfied by notnecessarilyunital
approximately subhomogeneous algebras of slow dimension growth.
Combined with results of the firstnamed author, this shows that
slow dimension growth coincides with $\mathcal Z$stability,
for approximately subhomogeneous algebras.
Keywords:nuclear C*algebras, Cuntz semigroup, dimension functions, stably projectionless C*algebras, approximately subhomogeneous C*algebras, slow dimension growth Categories:46L35, 46L05, 46L80, 47L40, 46L85 

23. CMB 2015 (vol 58 pp. 241)
 Botelho, Fernanda

Isometries and Hermitian Operators on Zygmund Spaces
In this paper we characterize the isometries of subspaces of the little Zygmund space. We show that the isometries of these spaces are surjective and represented as integral operators. We also show that all hermitian operators on these settings are bounded.
Keywords:Zygmund spaces, the little Zygmund space, Hermitian operators, surjective linear isometries, generators of oneparameter groups of surjective isometries Categories:46E15, 47B15, 47B38 

24. CMB 2014 (vol 58 pp. 91)
 Hasegawa, Kei

Essential Commutants of Semicrossed Products
Let $\alpha\colon G\curvearrowright M$ be a spatial action of countable
abelian group on a "spatial" von Neumann algebra $M$ and $S$ be its
unital subsemigroup with $G=S^{1}S$. We explicitly compute the
essential commutant and the essential fixedpoints, modulo the
Schatten $p$class or the compact operators, of the w$^*$semicrossed
product of $M$ by $S$ when $M'$ contains no nonzero compact
operators. We also prove a weaker result when $M$ is a von Neumann
algebra on a finite dimensional Hilbert space and
$(G,S)=(\mathbb{Z},\mathbb{Z}_+)$, which extends a famous result due
to Davidson (1977) for the classical analytic Toeplitz operators.
Keywords:essential commutant, semicrossed product Categories:47L65, 47A55 

25. CMB 2014 (vol 58 pp. 276)
 Johnson, William; Nasseri, Amir Bahman; Schechtman, Gideon; Tkocz, Tomasz

Injective Tauberian Operators on $L_1$ and Operators with Dense Range on $\ell_\infty$
There exist injective Tauberian operators on $L_1(0,1)$ that have
dense, nonclosed range. This gives injective, nonsurjective
operators on $\ell_\infty$ that have dense range. Consequently, there
are two quasicomplementary, noncomplementary subspaces of
$\ell_\infty$ that are isometric to $\ell_\infty$.
Keywords:$L_1$, Tauberian operator, $\ell_\infty$ Categories:46E30, 46B08, 47A53 
