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On complex interpolation and spectral continuity

Karen Saxe (1998)

Studia Mathematica

Let [ X 0 , X 1 ] t , 0 ≤ t ≤ 1, be Banach spaces obtained via complex interpolation. With suitable hypotheses, linear operators T that act boundedly on both X 0 and X 1 will act boundedly on each [ X 0 , X 1 ] t . Let T t denote such an operator when considered on [ X 0 , X 1 ] t , and σ ( T t ) denote its spectrum. We are motivated by the question of whether or not the map t → σ ( T t ) is continuous on (0,1); this question remains open. In this paper, we study continuity of two related maps: t → ( σ ( T t ) ) ∧ (polynomially convex hull) and t → ∂ e ( σ ( T t ) ) (boundary of the polynomially convex...

On duals of Calderón-Lozanovskiĭ intermediate spaces

Yves Raynaud (1997)

Studia Mathematica

We give a description of the dual of a Calderón-Lozanovskiĭ intermediate space φ(X,Y) of a couple of Banach Köthe function spaces as an intermediate space ψ(X*,Y*) of the duals, associated with a "variable" function ψ.

On equivalence of K- and J-methods for (n+1)-tuples of Banach spaces

Irina Asekritova, Natan Krugljak (1997)

Studia Mathematica

It is shown that the main results of the theory of real interpolation, i.e. the equivalence and reiteration theorems, can be extended from couples to a class of (n+1)-tuples of Banach spaces, which includes (n+1)-tuples of Banach function lattices, Sobolev and Besov spaces. As an application of our results, it is shown that Lions' problem on interpolation of subspaces and Semenov's problem on interpolation of subcouples have positive solutions when all spaces are Banach function lattices or their...

On extrapolation spaces

Giuseppe Da Prato, Pierre Grisvard (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si definisce un nuovo tipo di spazi a partire da un dato spazio di Banach X e da un operatore lineare A in X . Tali spazi si possono pensare come spazi di interpolazione D A ⁢ ( ϑ ) con ϑ negativo.

On interpolation of tensor products of Banach spaces.

Andreas Defant, Mieczyslaw Mastylo, Carsten Michels (2003)

RACSAM

For the complex interpolation method, Kouba proved an important interpolation formula for tensor products of Banach spaces. We give a partial extension of this formula in the injective case for the Gustavsson?Peetre method of interpolation within the setting of Banach function spaces.

On the ℒ -characteristic of fractional powers of linear operators

Jürgen Appell, Marilda A. Simões, Petr P. Zabrejko (1994)

Commentationes Mathematicae Universitatis Carolinae

We describe the geometric structure of the ℒ -characteristic of fractional powers of bounded or compact linear operators over domains with arbitrary measure. The description builds essentially on the Riesz-Thorin and Marcinkiewicz-Stein-Weiss- Ovchinnikov interpolation theorems, as well as on the Krasnosel’skij-Krejn factorization theorem.

On the range space of Yano's extrapolation theorem and new extrapolation estimates at infinity.

María Jesús Carro (2002)

Publicacions Matemàtiques

Given a sublinear operator T satisfying that ||Tf||Lp(ν) ≤ C/(p-1) ||f||Lp(μ), for every 1 < p ≤ p0, with C independent of f and p, it was proved in [C] that... [check the paper abstract for the formula]This estimate implies that T: L log L → B, where B is a rearrangement invariant space. The purpose of this note is to give several characterizations of the space B and study its associate space. This last information allows us to formulate an extrapolation result of Zygmund type for linear...

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