Operator ideal of Norlund-type sequence spaces

Type and Cotype of Operator Spaces

We consider two operator space versions of type and cotype, namely Sp-type, Sq-cotype and type (p, H), cotype (q, H) for a homogeneous Hilbertian operator space H and 1 ≤ p ≤ 2 ≤ q ≤ ∞, generalizing “OH-cotype 2” of G. Pisier. We compute type and cotype of some Hilbertian operator spaces and Lp spaces, and we investigate the relationship between a homogeneous Hilbertian space H and operator spa...

Some Ideal Convergent Sequence Spaces of Fuzzy Real Numbers

The concept of fuzzy sets was initially introduced by Zadeh[6]. It has a wide range of application in almost all branches of study, in particular in science, where mathematics is used. Now the notion of fuzzyness is used by many researcher in cybernetics, artificial intelligence, expert systems and fuzzy control, pattern recognition, operation research, decision making, image analysis, projecti...

A Maurey Type Result for Operator Spaces

The little Grothendieck theorem for Banach spaces says that every bounded linear operator between C(K) and l2 is 2-summing. However, it is shown in [7] that the operator space analogue fails. Not every cb-map v : K → OH is completely 2-summing. In this paper, we show an operator space analogue of Maurey’s theorem : Every cb-map v : K → OH is (q, cb)-summing for any q > 2 and hence admits a fact...

Lower bounds of Copson type for the transpose of matrices on weighted sequence spaces

Estimates of Essential Norms of Weighted Composition Operator from Bloch Type Spaces to Zygmund Type Spaces

Let u be a holomorphic function and φ a holomorphic self-map of the open unit disk D in the complex plane. We give some new characterizations for the boundedness of the weighted composition operators uCφ from Bloch type spaces to Zygmund type spaces in D in terms of u,φ, their derivatives and the n-th power φ of φ. Moreover, we obtain some similar estimates for their essential norms. From which...