A Unified Factorization Theorem for Lipschitz Summing Operators
نویسندگان
چکیده
منابع مشابه
LIPSCHITZ 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 Composition Theorem for Multiple Summing Operators
We prove that the composition S(u1, . . . , un) of a multilinear multiple 2-summing operator S with 2-summing linear operators uj is nuclear, generalizing a linear result of Grothendieck.
متن کاملREMARKS 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.
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 < ∞...
متن کاملFactorization for Non-symmetric Operators and Exponential H-theorem
We present a factorization method for estimating resolvents of nonsymmetric operators in Banach or Hilbert spaces in terms of estimates in another (typically smaller) “reference” space. This applies to a class of operators writing as a “regularizing” part (in a broad sense) plus a dissipative part. Then in the Hilbert case we combine this factorization approach with an abstract Plancherel ident...
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ژورنال
عنوان ژورنال: The Quarterly Journal of Mathematics
سال: 2019
ISSN: 0033-5606,1464-3847
DOI: 10.1093/qmathj/haz030