A criterion for compositions of (p,q)-absolutely summing operators to be compact
نویسندگان
چکیده
منابع مشابه
A General Extrapolation Theorem for Absolutely Summing Operators
The notion of absolutely (p; q)-summing linear operators is due to A. Pietsch [18] and B. Mitiagin and A. Pe lczyński [14], inspired by previous works of A. Grothendieck. The nonlinear theory of absolutely summing operators was initiated by A. Pietsch and a complete nonlinear approach was introduced by M.C. Matos [12]. Let X,Y be Banach spaces over a fixed scalar field K = R or C; for 1 ≤ p < ∞...
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Pietsch [5] introduced the concept of absolutely summing operators in Banach spaces and later in [6] extended this concept to absolutely p-summing operators. At the background of these concepts are the sequence spaces I p and their duality theory. The object of the present paper is to extend the above concept to abstract sequence spaces 2. The sequence spaces 2 involved are described in Section...
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Let E be a Banach space that does not contain any copy of l and A be a non commutative C∗-algebra. We prove that every absolutely summing operator from A into E∗ is compact, thus answering a question of Pe lczynski. As application, we show that if G is a compact metrizable abelian group and Λ is a Riesz subset of its dual then every countably additiveA∗-valued measure with bounded variation and...
متن کاملOn Weakly Measurable Stochastic Processes and Absolutely Summing Operators
A linear and continuous operator between Banach spaces is said to be absolutely summing if it maps unconditionally convergent series into absolutely convergent series. Moreover, it improves properties of stochastic processes. Indeed, N.Ghoussoub in [7] proved that an operator is absolutely summing if and only if it maps amarts (asymptotic martingales) into uniform amarts. In this paper we go a ...
متن کاملA Remark on Absolutely Summing Multilinear Mappings *
In this note we obtain new coincidence theorems for absolutely summing multilinear mappings between Banach spaces. We also prove that our results, in general, can not be improved.
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 1976
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-54-3-291-300