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3  Approximate Amenability of Segal Algebras II Alaghmandan, Mahmood
We prove that every proper Segal algebra of a SIN group is not
approximately amenable.


7  Characters on $C(X)$ Boulabiar, Karim
The precise condition on a completely regular space $X$ for every character on
$C(X) $ to be an evaluation at some point in $X$ is that $X$ be
realcompact. Usually, this classical result is obtained relying heavily on
involved (and even nonconstructive) extension arguments. This note provides a
direct proof that is accessible to a large audience.


9  Irreducible Tuples Without the Boundary Property Chavan, Sameer
We examine spectral behavior of irreducible tuples which do not
admit boundary property. In particular, we prove under some mild
assumption that the spectral radius of such an $m$tuple $(T_1,
\dots, T_m)$ must be the operator norm of $T^*_1T_1 + \cdots +
T^*_mT_m$. We use this simple observation to ensure boundary
property for an irreducible, essentially normal joint $q$isometry provided it
is not a joint isometry.
We further exhibit a family of
reproducing Hilbert $\mathbb{C}[z_1, \dots, z_m]$modules (of which
the DruryArveson Hilbert module is a prototype) with the property that any
two nested unitarily equivalent submodules are indeed equal.


19  Compact Commutators of Rough Singular Integral Operators Chen, Jiecheng; Hu, Guoen
Let $b\in \mathrm{BMO}(\mathbb{R}^n)$ and $T_{\Omega}$ be the singular
integral operator with kernel $\frac{\Omega(x)}{x^n}$, where
$\Omega$ is homogeneous of degree zero, integrable and has mean
value zero on the unit sphere $S^{n1}$. In this paper, by Fourier
transform estimates and approximation to the operator $T_{\Omega}$
by integral operators with smooth kernels, it is proved that if
$b\in \mathrm{CMO}(\mathbb{R}^n)$ and $\Omega$ satisfies a certain
minimal size condition, then the commutator generated by $b$ and
$T_{\Omega}$ is a compact operator on $L^p(\mathbb{R}^n)$ for
appropriate index $p$. The associated maximal operator is also
considered.


30  On an Exponential Functional Inequality and its Distributional Version Chung, Jaeyoung
Let $G$ be a group and $\mathbb K=\mathbb C$ or $\mathbb
R$.
In this article, as a generalization of the result of Albert
and Baker,
we investigate the behavior of bounded
and unbounded functions $f\colon G\to \mathbb K$ satisfying the inequality
$
\Biglf
\Bigl(\sum_{k=1}^n x_k
\Bigr)\prod_{k=1}^n f(x_k)
\Bigr\le \phi(x_2, \dots, x_n),\quad \forall\, x_1, \dots,
x_n\in G,
$
where $\phi\colon G^{n1}\to [0, \infty)$. Also, as a distributional
version of the above inequality we consider the stability of
the functional equation
\begin{equation*}
u\circ S  \overbrace{u\otimes \cdots \otimes u}^{n\text {times}}=0,
\end{equation*}
where $u$ is a Schwartz distribution or Gelfand hyperfunction,
$\circ$ and $\otimes$ are the pullback and tensor product of
distributions, respectively, and $S(x_1, \dots, x_n)=x_1+ \dots
+x_n$.


44  Orbits of Geometric Descent Daniilidis, A.; Drusvyatskiy, D.; Lewis, A. S.
We prove that quasiconvex functions always admit descent trajectories
bypassing all nonminimizing critical points.


51  Spectral Flows of Dilations of Fredholm Operators De Nitties, Giuseppe; SchulzBaldes, Hermann
Given an essentially unitary contraction and an arbitrary unitary
dilation of it, there is a naturally associated spectral flow which is
shown to be equal to the index of the operator. This result is
interpreted in terms of the $K$theory of an associated mapping
cone. It is then extended to connect $\mathbb{Z}_2$ indices of odd symmetric
Fredholm operators to a $\mathbb{Z}_2$valued spectral flow.


69  Correction to "Infinite Dimensional DeWitt Supergroups and Their Bodies" Fulp, Ronald Owen
The Theorem below is a correction to Theorem
3.5 in the article
entitled " Infinite Dimensional DeWitt Supergroups and Their
Bodies" published
in Canad. Math. Bull. Vol. 57 (2) 2014 pp. 283288. Only part
(iii) of that Theorem
requires correction. The proof of Theorem 3.5 in the original
article failed to separate
the proof of (ii) from the proof of (iii). The proof of (ii)
is complete once it is established
that $ad_a$ is quasinilpotent for each $a$ since it immediately
follows that $K$
is quasinilpotent. The proof of (iii) is not complete
in the original article. The revision appears as the proof of
(iii) of the revised Theorem below.


71  Limited Sets and Bibasic Sequences Ghenciu, Ioana
Bibasic sequences are used to study relative weak compactness
and relative norm compactness of limited sets.


80  The Equivariant Cohomology Rings of Peterson Varieties in All Lie
Types Harada, Megumi; Horiguchi, Tatsuya; Masuda, Mikiya
Let $G$ be a complex semisimple linear algebraic group and let
$Pet$ be the associated Peterson variety in the flag
variety $G/B$.
The main theorem of this note gives an efficient presentation
of the equivariant cohomology ring $H^*_S(Pet)$ of the
Peterson variety as a quotient of a polynomial ring by an ideal
$J$ generated by quadratic polynomials, in the spirit of the
Borel presentation of the cohomology of the flag variety. Here
the group $S \cong \mathbb{C}^*$ is a certain subgroup of a maximal
torus $T$ of $G$.
Our description of the ideal $J$ uses the Cartan matrix and is
uniform across Lie types. In our arguments we use the Monk formula
and Giambelli formula for the equivariant cohomology rings of
Peterson varieties for all Lie types, as obtained in the work
of Drellich. Our result generalizes a previous theorem of FukukawaHaradaMasuda,
which was only for Lie type $A$.


91  Essential Commutants of Semicrossed Products Hasegawa, Kei
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.


105  On Graphs Associated with Character Degrees and Conjugacy Class Sizes of Direct Products of Finite Groups HosseinZadeh, Samaneh; Iranmanesh, Ali; Hosseinzadeh, Mohammad Ali; Lewis, Mark L.
The prime vertex graph, $\Delta (X)$, and the common divisor graph,
$\Gamma (X)$, are two graphs that have been defined on a set of
positive integers $X$.
Some
properties of these graphs have been studied in the cases where either
$X$ is the set of character degrees of a group or $X$ is the set of
conjugacy class sizes of a group. In this paper, we gather some
results on these graphs arising in the context of direct product of
two groups.


110  Property T and Amenable Transformation Group $C^*$algebras Kamalov, F.
It is well known that a discrete group which is both amenable and
has Kazhdan's Property T must be finite. In this note we generalize
the above statement to the case of transformation groups. We show
that if $G$ is a discrete amenable group acting on a compact
Hausdorff space $X$, then the transformation group $C^*$algebra
$C^*(X, G)$ has Property T if and only if both $X$ and $G$ are finite. Our
approach does not rely on the use of tracial states on $C^*(X, G)$.


115  Weak Arithmetic Equivalence MantillaSoler, Guillermo
Inspired by the invariant of a number field given by its zeta
function, we define the notion of weak arithmetic equivalence and show
that under certain ramification hypotheses, this equivalence
determines the local root numbers of the number field. This is
analogous to a result of Rohrlich on the local root numbers of a
rational elliptic curve. Additionally, we prove that for tame
nontotally real number fields, the integral trace form is invariant
under arithmetic equivalence.


128  A Sharp Constant for the Bergman Projection Marković, Marijan
For the Bergman projection operator $P$ we prove that
\begin{equation*}
\P\colon L^1(B,d\lambda)\rightarrow B_1\ = \frac {(2n+1)!}{n!}.
\end{equation*}
Here $\lambda$ stands for the hyperbolic metric in the unit ball $B$ of
$\mathbb{C}^n$, and $B_1$ denotes the Besov space with an adequate
seminorm. We also consider a generalization of this result. This generalizes
some recent results due to Perälä.


134  On the Generalized AuslanderReiten Conjecture under Certain Ring Extensions Nasseh, Saeed
We show under some conditions that a Gorenstein ring $R$ satisfies the
Generalized AuslanderReiten Conjecture if and only if so does
$R[x]$. When $R$ is a local ring we prove the same result for some
localizations of $R[x]$.


144  Localization and Completeness in $L_2({\mathbb R})$ Olevskii, Victor
We give a necessary and sufficient condition for a sequence
to be a localization set for a determining average sampler.


150  Connections Between Metric Characterizations of Superreflexivity and the RadonNikodý Property for Dual Banach Spaces
Ostrovskii, Mikhail I.
Johnson and Schechtman (2009)
characterized superreflexivity in terms of finite diamond graphs.
The present author characterized the RadonNikodým property
(RNP) for dual spaces in terms of the infinite diamond. This
paper
is devoted to further study of relations between metric
characterizations of superreflexivity and the RNP for dual spaces.
The main result is that finite subsets of any set $M$ whose
embeddability characterizes the RNP for dual spaces, characterize
superreflexivity. It is also observed that the converse statement
does not hold, and that $M=\ell_2$ is a counterexample.


158  Corrigendum to "Chen Inequalities for Submanifolds of Real Space Forms with a Semisymmetric Nonmetric Connection" Özgür, Cihan; Mihai, Adela
We fix the coefficients in the inequality (4.1) in the Theorem 4.1(i) from
A. Mihai and C. zgür, "Chen inequalities for
submanifolds of real space forms with a semisymmetric nonmetric
connection" Canad. Math. Bull. 55 (2012), no. 3, 611622.


160  Some Normal Numbers Generated by Arithmetic Functions Pollack, Paul; Vandehey, Joseph
Let $g \geq 2$. A real number is said to be $g$normal if its base $g$ expansion contains every finite sequence of digits with the expected limiting frequency. Let $\phi$ denote Euler's totient function, let $\sigma$ be the sumofdivisors function, and let $\lambda$ be Carmichael's lambdafunction. We show that if $f$ is any function formed by composing $\phi$, $\sigma$, or $\lambda$, then the number
\[ 0. f(1) f(2) f(3) \dots \]
obtained by concatenating the base $g$ digits of successive $f$values is $g$normal. We also prove the same result if the inputs $1, 2, 3, \dots$ are replaced with the primes $2, 3, 5, \dots$. The proof is an adaptation of a method introduced by Copeland and Erdős in 1946 to prove the $10$normality of $0.235711131719\ldots$.


174  Periodic Solutions of Almost Linear Volterra Integrodynamic Equation on Periodic Time Scales Raffoul, Youssef N.
Using Krasnoselskii's fixed point theorem, we deduce
the existence of periodic solutions of nonlinear system of integrodynamic
equations on periodic time scales. These equations are
studied under a set of assumptions on the functions involved
in the
equations. The equations will be called almost linear when these
assumptions hold. The results of this papers are new for the
continuous and discrete time scales.


182  On Finite Groups with Dismantlable Subgroup Lattices Tărnăuceanu, Marius
In this note we study the finite groups whose subgroup
lattices are dismantlable.


188  Telescoping Estimates for Smooth Series Wirths, Karl Joachim
We derive telescoping majorants and minorants for some classes
of series and give applications of these results.


196  Dihedral Groups of order $2p$ of Automorphisms of Compact Riemann Surfaces of Genus $p1$ Yang, Qingjie; Zhong, Weiting
In this paper we prove that there is only one conjugacy class of
dihedral group of order $2p$ in the $2(p1)\times 2(p1)$ integral
symplectic group can be realized by an analytic automorphism
group
of compact connected Riemann surfaces of genus $p1$. A pair of
representative generators of the realizable class is also given.


207  Exact and Approximate Operator Parallelism Moslehian, Mohammad Sal; Zamani, Ali
Extending the notion of parallelism we introduce the concept of
approximate parallelism in normed spaces and then substantially
restrict ourselves to the setting of Hilbert space operators endowed
with the operator norm. We present several characterizations of the
exact and approximate operator parallelism in the algebra
$\mathbb{B}(\mathscr{H})$ of bounded linear operators acting on a
Hilbert space $\mathscr{H}$. Among other things, we investigate the
relationship between approximate parallelism and norm of inner
derivations on $\mathbb{B}(\mathscr{H})$. We also characterize the
parallel elements of a $C^*$algebra by using states. Finally we
utilize the linking algebra to give some equivalence assertions
regarding parallel elements in a Hilbert $C^*$module.

