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We present some properties of orthogonality and relate them with support disjoint and norm inequalities in p Schatten ideals. In addition, we investigate the problem of characterization of norm parallelism for bounded linear operators. We consider the characterization of norm parallelism problem in p Schatten ideals and locally uniformly convex spaces. Later on, we study the case when an operator is norm parallel to the identity operator. Finally, we give some equivalence assertions about the norm parallelism of compact operators. Some applications and generalizations are discussed for certain operators.
We construct a family $(mathcal{X}_al)_{alle omega_1}$ of reflexive Banach spaces with long transfinite bases but with no unconditional basic sequences. In our spaces $mathcal{X}_al$ every bounded operator $T$ is split into its diagonal part $D_T$ and its strictly singular part $S_T$.
We are concerned with surjectivity of perturbations of maximal monotone operators in non-reflexive Banach spaces. While in a reflexive setting, a classical surjectivity result due to Rockafellar gives a necessary and sufficient condition to maximal m
We characterize strong continuity of general operator semigroups on some Lebesgue spaces. In particular, a characterization of strong continuity of weighted composition semigroups on classical Hardy spaces and weighted Bergman spaces with regular wei
We prove that every isometry between two combinatorial spaces is determined by a permutation of the canonical unit basis combined with a change of signs. As a consequence, we show that in the case of Schreier spaces, all the isometries are given by a
Motivated by a general dilation theory for operator-valued measures, framings and bounded linear maps on operator algebras, we consider the dilation theory of the above objects with special structures. We show that every operator-valued system of imp