We use the injective envelope to study quasimultipliers of operator spaces. We prove that all representable operator algebra products that an operator space can be endowed with are induced by quasimultipliers. We obtain generalizations of the Banach-Stone theorem.

We show that noncommutative Lp-spaces satisfy the axioms of the (nonunital) operator system with a dominating constant 2 1 p . Therefore, noncommutative Lpspaces can be embedded into BpHq 2 1 p -completely isomorphically and complete order isomorphically.

In this paper we have examined the spectra of the operator D(r, 0, 0, s) on sequence spaces `p and bvp.

The dual spaces $d(p), 1 \lt p \infty ,$ of the discrete Cesaro (Banach) $\mathrm{ces} (q)$, $1 q were studied by G. Bennett, A. Jagers and others. These (reflexive) Banach induce non-normable Frechet $d (p+) := \bigcap_{r \gt p} d (r), $ for \leq (LB)-spaces (p-) \bigcup_{ r } recently introduced investigated in [11]. Here a detailed study is made various aspects, such as spectrum, continuity,...

The notion of B-convexity for operator spaces, which a priori depends on a set of parameters indexed by Σ, is defined. Some of the classical characterizations of this geometric notion for Banach spaces are studied in this new context. For instance, an operator space is BΣ-convex if and only if it has Σ-subtype. The class of uniformly non-L(Σ) operator spaces, which is also the class of BΣ-conve...

We generalize an important class of Banach spaces, namely the M embedded Banach spaces, to the non-commutative setting of operator spaces. The one-sided M -embedded operator spaces are the operator spaces which are one-sided M -ideals in their second dual. We show that several properties from the classical setting, like the stability under taking subspaces and quotients, unique extension proper...

This paper uses frame techniques to characterize the Schatten class properties of integral operators. The main result shows that if the coefficients {〈k,Φm,n〉} of certain frame expansions of the kernel k of an integral operator are in l, then the operator is Schatten p-class. As a corollary, we conclude that if the kernel or Kohn-Nirenberg symbol of a pseudodifferential operator lies in a parti...

The domination properties of elliptic invariant diierential operators on symmetric spaces of noncompact type are investigated. Using the relation between parametrices and fundamental solutions on symmetric space we will show that the invariant diierential operator applied to a function can be uniformly estimated by function and an elliptic operator of higher order applied to the function in L p...

Using recent characterizations of the compactness of composition operators on HardyOrlicz and Bergman-Orlicz spaces on the ball ([2, 3]), we first show that a composition operator which is compact on every Hardy-Orlicz (or Bergman-Orlicz) space has to be compact on H∞. Then, although it is well-known that a map whose range is contained in some nice Korányi approach region induces a compact comp...