Let Fn denote the free group with n generators g1, g2, . . . , gn. Let λ stand for the left regular representation of Fn and let τ be the standard trace associated to λ. Given any positive integer d, we study the operator space structure of the subspace Wp(n, d) of Lp(τ) generated by the family of operators λ(gi1gi2 · · · gid ) with 1 ≤ ik ≤ n. Moreover, our description of this operator space h...

Let $${\mathcal {H}}={\mathcal {H}}_+\oplus {\mathcal {H}}_-$$ be a fixed orthogonal decomposition of the complex separable Hilbert space {H}}$$ in two infinite-dimensional subspaces. We study geometry set {P}}^p$$ selfadjoint projections Banach algebra {A}}^p=\{A\in {B}}({\mathcal {H}}): [A,E_+]\in {B}}_p({\mathcal {H}})\},$$ where $$E_+$$ is projection onto {H}}_+$$ and {H}})$$ Schatten ideal...

Let T (t), 0 ≤ t < ∞, be a one parameter c0-semigroup of bounded linear operators on a Banach space X with infinitesimal generator A and R(λ, A) be the resolvent operator of A. The Hille-Yosida Theorem for c0-semigroups asserts that the resolvent operator of the infinitesimal generator A satisfies ‖R(λ, A)‖ ≤ M λ−ω for some constants M > 0 and λ ∈ R (the set of real numbers), λ > ω. The object ...

A Helson matrix is an infinite $A = (a_{m,n})_{m,n\geq1}$ such that the entry $a_{m,n}$ depends only on product $mn$. We demonstrate orthogonal projection from Hilbert--Schmidt class $\mathcal{S}_2$ onto subspace of matrices does not extend to a bounded operator Schatten $\mathcal{S}_q$ for $1 \leq q \neq 2 < \infty$. In fact, we prove more general result showing large natural projections are u...

In this paper, we completely characterize the compactness of Volterra type integration operators $$J_b$$ acting from weighted Bergman spaces $$A^p_{\alpha }$$ to Hardy $$H^q$$ for all $$0<p,q<\infty $$ . Furthermore, give some estimates essential norms $$J_b:A^p_{\alpha }\rightarrow H^q$$ in case $$0<p\le q<\infty We finally describe membership Schatten(-Herz) class operators.

The Schatten norm for the nuclear operator B*?B? was estimated from both sides. Here B? : L2 ? is Berezin transform regarding Fock spaces in plane. Also, we found case of unweighted Lebesgue spaces.

In this paper, we considered composition operators on weighted Hilbert spaces of analytic functions and  observed that a formula for the  essential norm, gives a Hilbert-Schmidt characterization and characterizes the membership in Schatten-class for these operators. Also, closed range composition operators  are investigated.

In this paper, we investigate singular integral operators induced by the Bergman kernel and Szegö on irreducible bounded symmetric domain in its standard Harish-Chandra realization. We completely characterize when Bergman-type Szegö-type belong to Schatten class operator ideals several analytic numerical invariants of domain. These results not only generalize a recent result Hilbert unit ball d...

In the recent years, the trace norm of graphs has been extensively studied under the name of graph energy. In this paper some of this research is extended to more general matrix norms, like the Schatten p-norms and the Ky Fan k-norms. Whenever possible the results are given both for graphs and general matrices. In various contexts a puzzling fact was observed: the Schatten p-norms are widely di...

In this paper, we investigate the known operator inequalities for p-Schatten norm and obtain some refinements of these when parameters taking values in different regions. Let A1,...,An, B1,..., Bn ? Bp(H) such that ?ni,j=1Ai*Bj=0. Then p 2, 21/p-?/4n3/p-?/4-1/2(?ni=1 ||Ai||4/?p + ?ni=1 ||Bi||4/?p )?/4 n2/p-1/2||?ni=1 |Ai|2 |Bi|2||1/2 p/2 n2/p-2/?(?ni,j=1 ||Ai Bj||?p)1/?. For 0 &lt; &gt; are rev...