We consider the class of integral operators Qφ on L (R+) of the form (Qφf)(x) = ∫ ∞ 0 φ(max{x, y})f(y)dy. We discuss necessary and sufficient conditions on φ to insure that Qφ is bounded, compact, or in the Schatten–von Neumann class Sp, 1 < p < ∞. We also give necessary and sufficient conditions for Qφ to be a finite rank operator. However, there is a kind of cut-off at p = 1, and for membersh...

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.

Let GL(n, C) ⊃ Un be the group of n× n complex valued invertible matrices and the subgroup of unitary matrices respectively. In this paper we study Finsler p-metrics on the homogeneous space Xn = GL(n, C)/Un for p ∈ [1,∞], which are induced by Schatten p-norms on the tangent bundle of Xn and are invariant under the action of GL(n, C). We show that for p ∈ (1,∞) the Busemann p-compactification i...

The related inequality (1.1) was obtained by Maher [3, Theorem 3.2] who showed that, if A is normal and AT = TA, where T ∈ Cp , then ‖T − (AX −XA)‖p ≥ ‖T‖p for all X ∈ ( ), where Cp is the von Neumann-Schatten class, 1≤ p <∞, and ‖·‖p its norm. Here we show that Maher’s result is also true in the case where Cp is replaced by ( ), the ideal of all compact operators with ‖·‖∞ its norm.Which allow...

Let ‖ · ‖ be a unitary similarity invariant norm on the set Mn of n× n complex matrices. A description is obtained for surjective maps φ on Mn satisfying ‖AB− BA‖ = ‖φ(A)φ(B)−φ(B)φ(A)‖ for all A,B ∈ Mn . The general theorem covers the special cases when the norm is one of the Schatten p -norms, the Ky-Fan k -norms, or the k -numerical radii. Mathematics subject classification (2000): Primary 15...

Let En ⊂ L 1 be the n-dimensional subspace which appeared in Kašin’s theorem such that L 1 = En ⊕E⊥ n and the L 1 and L 2 norms are universally equivalent on both En and E⊥ n . In this paper, we introduce and study some properties concerning extension and weak Grothendieck’s theorem (WGT). We show that the Schatten space Sp for all 0 < p ≤ ∞ does not verify the theorem of extension. We prove al...

We study the first and second orders of asymptotic expansion, as dimension goes to infinity, moments Hilbert-Schmidt norm a uniformly distributed matrix in p-Schatten unit ball. consider case matrices with real, complex or quaternionic entries, self-adjoint not. When p>3, this expansion allows us establish generalized version variance conjecture for family balls matrices.