Search: MSC category 47B10
( Operators belonging to operator ideals (nuclear, $p$summing, in the Schattenvon Neumann classes, etc.) [See also 47L20] )
1. CMB 2010 (vol 54 pp. 21)
 Bouali, S.; Echchad, M.

Generalized Dsymmetric Operators II
Let $H$ be a separable,
infinitedimensional, complex Hilbert space and let $A, B\in{\mathcal L
}(H)$, where ${\mathcal L}(H)$ is the algebra of all bounded linear
operators on $H$. Let $\delta_{AB}\colon {\mathcal L}(H)\rightarrow {\mathcal
L}(H)$ denote the generalized derivation $\delta_{AB}(X)=AXXB$.
This note will initiate a study on the class of pairs $(A,B)$ such
that $\overline{{\mathcal R}(\delta_{AB})}= \overline{{\mathcal
R}(\delta_{A^{\ast}B^{\ast}})}$.
Keywords:generalized derivation, adjoint, Dsymmetric operator, normal operator Categories:47B47, 47B10, 47A30 

2. CMB 2008 (vol 51 pp. 67)
 Kalton, Nigel; Sukochev, Fyodor

RearrangementInvariant Functionals with Applications to Traces on Symmetrically Normed Ideals
We present a construction of singular rearrangement
invariant functionals on Marcinkiewicz function/operator spaces.
The functionals constructed differ from all previous examples in
the literature in that they fail to be symmetric. In other words,
the functional $\phi$ fails the condition that if $x\pprec y$
(HardyLittlewoodPolya submajorization) and $0\leq x,y$, then
$0\le \phi(x)\le \phi(y).$ We apply our results to singular traces
on symmetric operator spaces (in particular on
symmetricallynormed ideals of compact operators), answering
questions raised by Guido and Isola.
Categories:46L52, 47B10, 46E30 

3. CMB 2007 (vol 50 pp. 85)
 Han, Deguang

Classification of Finite GroupFrames and SuperFrames
Given a finite group $G$, we examine the classification of all
frame representations of $G$ and the classification of all
$G$frames, \emph{i.e.,} frames induced by group representations of $G$.
We show that the exact number of equivalence classes of $G$frames
and the exact number of frame representations can be explicitly
calculated. We also discuss how to calculate the largest number
$L$ such that there exists an $L$tuple of strongly disjoint
$G$frames.
Keywords:frames, groupframes, frame representations, disjoint frames Categories:42C15, 46C05, 47B10 

4. CMB 2004 (vol 47 pp. 144)
 Xia, Jingbo

On the Uniqueness of Wave Operators Associated With NonTrace Class Perturbations
Voiculescu has previously established the uniqueness of the wave operator
for the problem of $\mathcal{C}^{(0)}$perturbation of commuting tuples
of selfadjoint operators in the case where the norm ideal $\mathcal{C}$
has the property $\lim_{n\rightarrow\infty} n^{1/2}\P_n\_{\mathcal{C}}=0$,
where $\{P_n\}$ is any sequence of orthogonal projections with $\rank(P_n)=n$.
We prove that the same uniqueness result holds true so long as $\mathcal{C}$
is not the trace class. (It is well known that there is no such uniqueness
in the case of traceclass perturbation.)
Categories:47A40, 47B10 

5. CMB 2004 (vol 47 pp. 49)
 Lindström, Mikael; Makhmutov, Shamil; Taskinen, Jari

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
Keywords:Bloch space, little Bloch space, $\BMOA$, $\VMOA$, $Q_p$ spaces,, composition operator, compact operator, essential norm Categories:47B38, 47B10, 46E40, 46E15 

6. CMB 1999 (vol 42 pp. 162)
7. CMB 1999 (vol 42 pp. 87)
 Kittaneh, Fuad

Some norm inequalities for operators
Let $A_i$, $B_i$ and $X_i$ $(i=1, 2, \dots, n)$ be operators on a
separable Hilbert space. It is shown that if $f$ and $g$ are
nonnegative continuous functions on $[0,\infty)$ which satisfy the
relation $f(t)g(t) =t$ for all $t$ in $[0,\infty)$, then
$$
\Biglvert \,\Bigl\sum^n_{i=1} A^*_i X_i B_i \Bigr^r \,\Bigrvert^2
\leq \Biglvert \Bigl( \sum^n_{i=1} A^*_i f (X^*_i)^2 A_i \Bigr)^r
\Bigrvert \, \Biglvert \Bigl( \sum^n_{i=1} B^*_i g (X_i)^2 B_i
\Bigr)^r \Bigrvert
$$
for every $r>0$ and for every unitarily invariant norm. This result
improves some known CauchySchwarz type inequalities. Norm
inequalities related to the arithmeticgeometric mean inequality and
the classical Heinz inequalities are also obtained.
Keywords:Unitarily invariant norm, positive operator, arithmeticgeometric mean inequality, CauchySchwarz inequality, Heinz inequality Categories:47A30, 47B10, 47B15, 47B20 
