Let ‎X be an ‎‎n-‎‎‎‎‎‎square complex matrix with the ‎Cartesian decomposition ‎‎X = A + i ‎B‎‎‎‎‎, ‎where ‎‎A ‎and ‎‎B ‎are ‎‎‎n ‎‎times n‎ ‎Hermitian ‎matrices. ‎It ‎is ‎known ‎that ‎‎$Vert X Vert_p^2 ‎leq 2(Vert A Vert_p^2 + Vert B Vert_p^2)‎‎‎$, ‎where ‎‎$‎p ‎‎geq 2‎$‎ ‎and ‎‎$‎‎Vert . Vert_p$ ‎is ‎the ‎Schatten ‎‎‎‎p-norm.‎ ‎‎ ‎‎In this paper‎, this inequality and some of its improvements ...

Abstract We characterize the Hilbert–Schmidt class membership of commutator with Hilbert transform in two weight setting. The characterization depends upon symbol being a new weighted Besov space. This follows from Schatten S p result for dyadic paraproducts, where $1&lt; &lt; \infty $ 1 &lt; p</...

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...

We discuss Arens regularity of the projective tensor product Banach algebras consisting Schatten class operators. More precisely, exploiting Ülger’s biregularity criterion, we prove that for any Hilbert space ℋ, Sp(ℋ)⊗γ Sq (ℋ) and B(S2(ℋ))⊗γ S2(ℋ) are not regular every pair 1≤p,q≤2; whereas, when ℋ is separable equipped with Schur product, show completely continuous S2(ℋ)⊗γ regular.

We prove a Banach version of Garland's method proving vanishing cohomology for groups acting on simplicial complexes. The novelty this new is that our condition applies to every reflexive space. This allows us deduce several criteria group with coefficients in classes spaces (uniformly curved spaces, Hilbertian and $L^p$ spaces). Using these criteria, we improve recent results regarding fixed p...

In this paper we study general Schatten-p quasi-norm (SPQN) regularized matrix minimization problems. In particular, we first introduce a class of first-order stationary points for them, and show that the first-order stationary points introduced in [11] for an SPQN regularized vector minimization problem are equivalent to those of an SPQN regularized matrix minimization reformulation. We also s...