A general one-sided compactness result for interpolation of bilinear operators

2019 ◽  
Vol 124 (2) ◽  
pp. 247-262
Author(s):  
Eduardo Brandani Da Silva ◽  
Dicesar Lass Fernandez
Keyword(s):  
Banach Spaces ◽  
Interpolation Method ◽  
Compactness Theorem ◽  
Compactness Result ◽  
Interpolation Of Banach Spaces ◽  
Bilinear Operators

The behavior of bilinear operators acting on the interpolation of Banach spaces in relation to compactness is analyzed, and an one-sided compactness theorem is obtained for bilinear operators interpolated by the ρ interpolation method.

Real Interpolation of Banach Spaces

1996 ◽  
pp. 29-72
Author(s):  
Werner O. Amrein ◽  
Anne Boutet Monvel ◽  
Vladimir Georgescu
Keyword(s):  
Banach Spaces ◽  
Real Interpolation ◽  
Interpolation Of Banach Spaces

scholarly journals ON THE STABILITY OF THE DIFFERENTIAL PROCESS GENERATED BY COMPLEX INTERPOLATION

2020 ◽  
pp. 1-32
Author(s):  
Jesús M. F. Castillo ◽  
Willian H. G. Corrêa ◽  
Valentin Ferenczi ◽  
Manuel González
Keyword(s):  
Unit Circle ◽  
Banach Spaces ◽  
Local Stability ◽  
Interpolation Method ◽  
Complex Interpolation ◽  
Analytic Family ◽  
Köthe Spaces ◽  
The Stability ◽  
Stability Results ◽  
Differential Process

We study the stability of the differential process of Rochberg and Weiss associated with an analytic family of Banach spaces obtained using the complex interpolation method for families. In the context of Köthe function spaces, we complete earlier results of Kalton (who showed that there is global bounded stability for pairs of Köthe spaces) by showing that there is global (bounded) stability for families of up to three Köthe spaces distributed in arcs on the unit circle while there is no (bounded) stability for families of four or more Köthe spaces. In the context of arbitrary pairs of Banach spaces, we present some local stability results and some global isometric stability results.

Martin's axiom in the model theory of LA

1980 ◽  
Vol 45 (1) ◽  
pp. 172-176
Author(s):  
W. Richard Stark
Keyword(s):  
Model Theory ◽  
Equivalence Theorem ◽  
Compactness Theorem ◽  
Compactness Result ◽  
First Order ◽  
Martin's Axiom ◽  
New Class ◽  
Martin’S Axiom ◽  
Order Language ◽  
Omitting Types

Working in ZFC + Martin's Axiom we develop a generalization of the Barwise Compactness Theorem which holds in languages of cardinality less than . Next, using this compactness theorem, an omitting types theorem for fewer than types is proved. Finally, in ZFC, we prove that this compactness result implies Martin's Axiom (the Equivalence Theorem). Our compactness theorem applies to a new class of theories—ccΣ-theories—which generalize the countable Σ-theories of Barwise's theorem. The Omitting Types Theorem and the Equivalence Theorem serve as examples illustrating the use of ccΣ-theories.Assume = (A, ε) or = (A, ε R1,…,Rm) where is admissible. L() is the first-order language with constants for elements of A and relation symbols for relations in . LA is A ⋂ L∞ω where the L of L∞ω is any language in A. A theory T in LA is consistent if there is no derivation in A of a contradiction from T. is LA with new constants ca for each a and A. The basic terms of consist of the constants of and the terms f(ca1,…,cam) built directly from constants using functions f of . The symbol t is used for basic terms. A theory T in LA is Σ if it is defined by a formula of L(). The formula φ⌝ is a logical equivalent of ¬φ defined by: (1) φ⌝ = ¬φ if φ is atomic; (2) (¬φ)⌝ = φ (3) (⋁φ∈Φ φ)⌝ = ⋀φ∈Φ φ⌝; (4) (⋀φ∈Φ φ) ⋁φ∈Φ φ⌝; (5) (∃χφ(x))⌝ ∀χφ⌝(x); ∀χφ(x))⌝ = ∃χφ⌝(x).

Interpolation of Banach Spaces, Perron Processes, and Yang-Mills

1993 ◽  
Vol 115 (2) ◽  
pp. 243 ◽  
Author(s):  
R. R. Coifman ◽  
S. Semmes
Keyword(s):  
Banach Spaces ◽  
Interpolation Of Banach Spaces ◽  
Yang Mills

Real Interpolation with Logarithmic Functors and Reiteration

2000 ◽  
Vol 52 (5) ◽  
pp. 920-960 ◽  
Author(s):  
W. D. Evans ◽  
B. Opic
Keyword(s):  
Banach Spaces ◽  
Interpolation Method ◽  
Real Interpolation ◽  
Real Interpolation Method ◽  
Original Scale ◽  
Limiting Values

AbstractWe present “reiteration theorems” with limiting values θ = 0 and θ = 1 for a real interpolation method involving broken-logarithmic functors. The resulting spaces lie outside of the original scale of spaces and to describe them new interpolation functors are introduced. For an ordered couple of (quasi-) Banach spaces similar results were presented without proofs by Doktorskii in [D].

Interpolation of Bilinear Operators Between Quasi-Banach Spaces

Positivity ◽  
2006 ◽  
Vol 10 (3) ◽  
pp. 409-429 ◽  
Author(s):  
Loukas Grafakos ◽  
Mieczysław Mastyło
Keyword(s):  
Banach Spaces ◽  
Bilinear Operators
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