Some remarks on p-absolutely summing operators
نویسندگان
چکیده
منابع مشابه
REMARKS ON LIPSCHITZ p-SUMMING OPERATORS
In this note, a nonlinear version of the Extrapolation Theorem is proved and as a corollary, a nonlinear version of the Grothendieck’s Theorem is presented. Finally, we prove that if T : X → H is Lipschitz with X being a pointed metric space and T (0) = 0 such that T∣H∗ is q-summing (1 ≤ q <∞), then T is Lipschitz 1-summing.
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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...
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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 کاملLIPSCHITZ p-SUMMING OPERATORS
The notion of Lipschitz p-summing operator is introduced. A non linear Pietsch factorization theorem is proved for such operators and it is shown that a Lipschitz p-summing operator that is linear is a p-summing operator in the usual sense.
متن کاملA 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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ژورنال
عنوان ژورنال: Hokkaido Mathematical Journal
سال: 1976
ISSN: 0385-4035
DOI: 10.14492/hokmj/1381758680