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Real interpolation and compactness.

Fernando Cobos Díaz (1989)

Revista Matemática de la Universidad Complutense de Madrid

The behavior of compactness under real interpolation real is discussed. Classical results due to Krasnoselskii, Lions-Peetre, Persson, and Hayakawa are described, as well as others obtained very recently by Edmunds, Potter, Fernández, and the author.

Real Interpolation between Row and Column Spaces

Gilles Pisier (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

We give an equivalent expression for the K-functional associated to the pair of operator spaces (R,C) formed by the rows and columns respectively. This yields a description of the real interpolation spaces for the pair (Mₙ(R),Mₙ(C)) (uniformly over n). More generally, the same result is valid when Mₙ (or B(ℓ₂)) is replaced by any semi-finite von Neumann algebra. We prove a version of the non-commutative Khintchine inequalities (originally due to Lust-Piquard) that is valid for the Lorentz spaces...

Real interpolation for families of Banach spaces

Maria Carro (1994)

Studia Mathematica

We develop a new method of real interpolation for infinite families of Banach spaces that covers the methods of Lions-Peetre, Sparr for N spaces, Fernández for 2 N spaces and the recent method of Cobos-Peetre.

Real interpolation for non-distant Marcinkiewicz spaces.

Evgeniy Pustylnik (2001)

Revista Matemática Complutense

We describe the real interpolation spaces between given Marcinkiewicz spaces that have fundamental functions of the form t1/q (ln (e/t)a with the same exponent q. The spaces thus obtained are used for the proof of optimal interpolation theorem from [7], concerning spaces L∞,a,E.

Real linear isometries between function algebras. II

Osamu Hatori, Takeshi Miura (2013)

Open Mathematics

We describe the general form of isometries between uniformly closed function algebras on locally compact Hausdorff spaces in a continuation of the study by Miura. We can actually obtain the form on the Shilov boundary, rather than just on the Choquet boundary. We also give an example showing that the form cannot be extended to the whole maximal ideal space.

Real method of interpolation on subcouples of codimension one

S. V. Astashkin, P. Sunehag (2008)

Studia Mathematica

We find necessary and sufficient conditions under which the norms of the interpolation spaces ( N ₀ , N ₁ ) θ , q and ( X ₀ , X ₁ ) θ , q are equivalent on N, where N is the kernel of a nonzero functional ψ ∈ (X₀ ∩ X₁)* and N i is the normed space N with the norm inherited from X i (i = 0,1). Our proof is based on reducing the problem to its partial case studied by Ivanov and Kalton, where ψ is bounded on one of the endpoint spaces. As an application we completely resolve the problem of when the range of the operator T θ = S - 2 θ I (S denotes the...

Realcompactness and spaces of vector-valued functions

Jesus Araujo (2002)

Fundamenta Mathematicae

It is shown that the existence of a biseparating map between a large class of spaces of vector-valued continuous functions A(X,E) and A(Y,F) implies that some compactifications of X and Y are homeomorphic. In some cases, conditions are given to warrant the existence of a homeomorphism between the realcompactifications of X and Y; in particular we find remarkable differences with respect to the scalar context: namely, if E and F are infinite-dimensional and T: C*(X,E) → C*(Y,F) is a biseparating...

Real-linear isometries between certain subspaces of continuous functions

Arya Jamshidi, Fereshteh Sady (2013)

Open Mathematics

In this paper we first consider a real-linear isometry T from a certain subspace A of C(X) (endowed with supremum norm) into C(Y) where X and Y are compact Hausdorff spaces and give a result concerning the description of T whenever A is a uniform algebra on X. The result is improved for the case where T(A) is, in addition, a complex subspace of C(Y). We also give a similar description for the case where A is a function space on X and the range of T is a real subspace of C(Y) satisfying a ceratin...

Real-linear isometries between function algebras

Takeshi Miura (2011)

Open Mathematics

Let A and B be uniformly closed function algebras on locally compact Hausdorff spaces with Choquet boundaries Ch A and ChB, respectively. We prove that if T: A → B is a surjective real-linear isometry, then there exist a continuous function κ: ChB → z ∈ ℂ: |z| = 1, a (possibly empty) closed and open subset K of ChB and a homeomorphism φ: ChB → ChA such that T(f) = κ(f ∘φ) on K and T f = κ f o φ ¯ on ChB K for all f ∈ A. Such a representation holds for surjective real-linear isometries between (not necessarily...

Rearrangement of series in nonnuclear spaces

Wojciech Banaszczyk (1993)

Studia Mathematica

It is proved that if a metrizable locally convex space is not nuclear, then it does not satisfy the Lévy-Steinitz theorem on rearrangement of series.

Currently displaying 61 – 80 of 445