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1. CMB Online first
Compact Commutators of Rough Singular Integral Operators 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.
Keywords:commutator,singular integral operator, compact operator, maximal operator Category:42B20 
2. CMB 2013 (vol 57 pp. 546)
Compact Operators in Regular LCQ Groups We show that a regular locally compact quantum group $\mathbb{G}$ is discrete
if and only if $\mathcal{L}^{\infty}(\mathbb{G})$ contains nonzero compact operators on
$\mathcal{L}^{2}(\mathbb{G})$.
As a corollary we classify all discrete quantum groups among
regular locally compact quantum groups $\mathbb{G}$ where
$\mathcal{L}^{1}(\mathbb{G})$ has the RadonNikodym property.
Keywords:locally compact quantum groups, regularity, compact operators Category:46L89 
3. CMB 2012 (vol 57 pp. 25)
Subadditivity Inequalities for Compact Operators Some subadditivity inequalities for matrices and concave functions also hold for Hilbert space operators, but (unfortunately!) with an additional $\varepsilon$ term. It seems not possible to erase this residual term. However, in case of compact operators we show that the $\varepsilon$ term is unnecessary. Further, these inequalities are strict in a certain sense when some natural assumptions are satisfied. The discussion also stresses on matrices and their compressions and several open questions or conjectures are considered, both in the matrix and operator settings.
Keywords:concave or convex function, Hilbert space, unitary orbits, compact operators, compressions, matrix inequalities Categories:47A63, 15A45 
4. CMB 2012 (vol 56 pp. 503)
Weak Sequential Completeness of $\mathcal K(X,Y)$ For Banach spaces $X$ and $Y$, we show that if $X^\ast$ and $Y$ are
weakly sequentially complete and every weakly compact operator from
$X$ to $Y$ is compact then the space of all compact operators from $X$
to $Y$ is weakly sequentially complete. The converse is also true if,
in addition, either $X^\ast$ or $Y$ has the bounded compact
approximation property.
Keywords:weak sequential completeness, reflexivity, compact operator space Categories:46B25, 46B28 
5. CMB 2011 (vol 56 pp. 65)
The Uncomplemented Subspace $\mathbf K(X,Y) $ A vector measure result is used to study the complementation of the
space $K(X,Y)$ of compact operators in the spaces $W(X,Y)$ of weakly
compact operators, $CC(X,Y)$ of completely continuous operators, and
$U(X,Y)$ of unconditionally converging operators.
Results of Kalton and Emmanuele concerning the complementation of
$K(X,Y)$ in $L(X,Y)$ and in $W(X,Y)$ are generalized. The containment
of $c_0$ and $\ell_\infty$ in spaces of operators is also studied.
Keywords:compact operators, weakly compact operators, uncomplemented subspaces of operators Categories:46B20, 46B28 
6. CMB 2011 (vol 55 pp. 449)
Complemented Subspaces of Linear Bounded Operators We study the complementation of the space $W(X,Y)$ of weakly compact operators, the space $K(X,Y)$ of compact operators, the space $U(X,Y)$ of unconditionally converging operators, and the space $CC(X,Y)$ of completely continuous operators in the space $L(X,Y)$ of bounded linear operators from $X$ to $Y$.
Feder proved that if $X$ is infinitedimensional and $c_0
\hookrightarrow Y$, then $K(X,Y)$ is uncomplemented in
$L(X,Y)$. Emmanuele and John showed that if $c_0 \hookrightarrow
K(X,Y)$, then $K(X,Y)$ is uncomplemented in $L(X,Y)$.
Bator and Lewis showed that if $X$ is not a Grothendieck space and
$c_0 \hookrightarrow Y$, then $W(X,Y)$ is uncomplemented in
$L(X,Y)$. In this paper, classical results of Kalton and separably
determined operator ideals with property $(*)$ are used to obtain
complementation results that yield these theorems as corollaries.
Keywords:spaces of operators, complemented subspaces, compact operators, weakly compact operators, completely continuous operators Categories:46B20, 46B28 
7. CMB 2011 (vol 55 pp. 548)
Noncomplemented Spaces of Operators, Vector Measures, and $c_o$ The Banach spaces $L(X, Y)$, $K(X, Y)$, $L_{w^*}(X^*, Y)$, and
$K_{w^*}(X^*, Y)$ are studied to determine when they contain the
classical Banach spaces $c_o$ or $\ell_\infty$. The complementation of
the Banach space $K(X, Y)$ in $L(X, Y)$ is discussed as well as what
impact this complementation has on the embedding of $c_o$ or
$\ell_\infty$ in $K(X, Y)$ or $L(X, Y)$. Results of Kalton, Feder, and
Emmanuele concerning the complementation of $K(X, Y)$ in $L(X, Y)$ are
generalized. Results concerning the complementation of the Banach
space $K_{w^*}(X^*, Y)$ in $L_{w^*}(X^*, Y)$ are also explored as well
as how that complementation affects the embedding of $c_o$ or
$\ell_\infty$ in $K_{w^*}(X^*, Y)$ or $L_{w^*}(X^*, Y)$. The $\ell_p$
spaces for $1 = p < \infty$ are studied to determine when the space of
compact operators from one $\ell_p$ space to another contains
$c_o$. The paper contains a new result which classifies these spaces
of operators. A new result using vector measures is given to
provide more efficient proofs of theorems by Kalton, Feder, Emmanuele,
Emmanuele and John, and Bator and Lewis.
Keywords:spaces of operators, compact operators, complemented subspaces, $w^*w$compact operators Category:46B20 
8. CMB 2009 (vol 53 pp. 118)
The Uncomplemented Spaces $W(X,Y)$ and $K(X,Y)$ Classical results of Kalton and techniques of Feder are used to study the complementation of the space $W(X, Y)$ of weakly compact operators and the space $K(X,Y)$ of compact operators in the space $L(X,Y)$ of all bounded linear maps from X to Y.
Keywords:spaces of operators, complemented subspace, weakly compact operator, basic sequence Categories:46B28, 46B15, 46B20 
9. CMB 2008 (vol 51 pp. 15)
The Duality Problem for the Class of AMCompact Operators on Banach Lattices We prove the converse of a
theorem of Zaanen about the duality problem of
positive AMcompact operators.
Keywords:AMcompact operator, order continuous norm, discrete vector lattice Categories:46A40, 46B40, 46B42 
10. CMB 2004 (vol 47 pp. 298)
Near Triangularizability Implies Triangularizability In this paper we consider collections of
compact operators on a real or
complex Banach space including linear operators
on finitedimensional vector spaces. We show
that such a collection is simultaneously
triangularizable if and only if it is arbitrarily
close to a simultaneously triangularizable
collection of compact operators. As an application
of these results we obtain an invariant subspace
theorem for certain bounded operators. We
further prove that in finite dimensions near
reducibility implies reducibility whenever
the ground field is $\BR$ or $\BC$.
Keywords:Linear transformation, Compact operator,, Triangularizability, Banach space, Hilbert, space Categories:47A15, 47D03, 20M20 
11. CMB 2004 (vol 47 pp. 49)
The Essential Norm of a Blochto$Q_p$ Composition Operator The $Q_p$ spaces coincide with the Bloch space for $p>1$ and are
subspaces of $\BMOA$ for $0

12. CMB 1999 (vol 42 pp. 139)
Essential Norm and Weak Compactness of Composition Operators on Weighted Banach Spaces of Analytic Functions 
Essential Norm and Weak Compactness of Composition Operators on Weighted Banach Spaces of Analytic Functions Every weakly compact composition operator between weighted Banach
spaces $H_v^{\infty}$ of analytic functions with weighted supnorms is
compact. Lower and upper estimates of the essential norm of
continuous composition operators are obtained. The norms of the point
evaluation functionals on the Banach space $H_v^{\infty}$ are also
estimated, thus permitting to get new characterizations of compact
composition operators between these spaces.
Keywords:weighted Banach spaces of holomorphic functions, composition operator, compact operator, weakly compact operator Categories:47B38, 30D55, 46E15 