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Tameness in Fréchet spaces of analytic functions

Aydın Aytuna (2016)

Studia Mathematica

A Fréchet space with a sequence | | · | | k k = 1 ∞ of generating seminorms is called tame if there exists an increasing function σ: ℕ → ℕ such that for every continuous linear operator T from into itself, there exist N₀ and C > 0 such that | | T ( x ) | | ₙ ≤ C | | x | | σ ( n ) ∀x ∈ , n ≥ N₀. This property does not depend upon the choice of the fundamental system of seminorms for and is a property of the Fréchet space . In this paper we investigate tameness in the Fréchet spaces (M) of analytic functions on Stein manifolds M equipped with the compact-open...

Tensor product in symmetric function spaces.

S. V. Astashkin (1997)

Collectanea Mathematica

A concept of the multiplicator of symmetric function space concerning to projective tensor product is introduced and studied. This allows us to obtain some concrete results. In particular, the well-know theorem of R. O'Neil about boundedness of tensor product in the Lorentz spaces Lpq is discussed.

The angular distribution of mass by Bergman functions.

Donald E. Marshall, Wayne Smith (1999)

Revista Matemática Iberoamericana

Let D = {z: |z| < 1} be the unit disk in the complex plane and denote by dA two-dimensional Lebesgue measure on D. For ε > 0 we define Σε = {z: |arg z| < ε}. We prove that for every ε > 0 there exists a δ > 0 such that if f is analytic, univalent and area-integrable on D, and f(0) = 0 thenThis problem arose in connection with a characterization by Hamilton, Reich and Strebel of extremal dilatation for quasiconformal homeomorphisms of D.

The Banach algebra of continuous bounded functions with separable support

M. R. Koushesh (2012)

Studia Mathematica

We prove a commutative Gelfand-Naimark type theorem, by showing that the set C s ( X ) of continuous bounded (real or complex valued) functions with separable support on a locally separable metrizable space X (provided with the supremum norm) is a Banach algebra, isometrically isomorphic to C₀(Y) for some unique (up to homeomorphism) locally compact Hausdorff space Y. The space Y, which we explicitly construct as a subspace of the Stone-Čech compactification of X, is countably compact, and if X is non-separable,...

The Banach-Saks property in rearrangement invariant spaces

P. G. Dodds, E. M. Semenov, F. A. Sukochev (2004)

Studia Mathematica

This paper studies the Banach-Saks property in rearrangement invariant spaces on the positive half-line. A principal result of the paper shows that a separable rearrangement invariant space E with the Fatou property has the Banach-Saks property if and only if E has the Banach-Saks property for disjointly supported sequences. We show further that for Orlicz and Lorentz spaces, the Banach-Saks property is equivalent to separability although the separable parts of some Marcinkiewicz spaces fail the...

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