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Banach space properties of strongly tight uniform algebras

Scott Saccone (1995)

Studia Mathematica

We use the work of J. Bourgain to show that some uniform algebras of analytic functions have certain Banach space properties. If X is a Banach space, we say X is strongif X and X* have the Dunford-Pettis property, X has the Pełczyński property, and X* is weakly sequentially complete. Bourgain has shown that the ball-algebras and the polydisk-algebras are strong Banach spaces. Using Bourgain’s methods, Cima and Timoney have shown that if K is a compact planar set and A is R(K) or A(K), then A and...

Banach spaces

Laurent Gruson, Marius van der Put (1974)

Mémoires de la Société Mathématique de France

Banach spaces in which all multilinear forms are weakly sequentially continuous

Jesús Castillo, Ricardo García, Raquel Gonzalo (1999)

Studia Mathematica

We solve several problems in the theory of polynomials in Banach spaces. (i) There exist Banach spaces without the Dunford-Pettis property and without upper p-estimates in which all multilinear forms are weakly sequentially continuous: some Lorentz sequence spaces, their natural preduals and, most notably, the dual of Schreier's space. (ii) There exist Banach spaces X without the Dunford-Pettis property such that all multilinear forms on X and X* are weakly sequentially continuous; this gives an...

Biseparating maps on generalized Lipschitz spaces

Denny H. Leung (2010)

Studia Mathematica

Let X, Y be complete metric spaces and E, F be Banach spaces. A bijective linear operator from a space of E-valued functions on X to a space of F-valued functions on Y is said to be biseparating if f and g are disjoint if and only if Tf and Tg are disjoint. We introduce the class of generalized Lipschitz spaces, which includes as special cases the classes of Lipschitz, little Lipschitz and uniformly continuous functions. Linear biseparating maps between generalized Lipschitz spaces are characterized...

Bloch type spaces on the unit ball of a Hilbert space

Zhenghua Xu (2019)

Czechoslovak Mathematical Journal

We initiate the study of Bloch type spaces on the unit ball of a Hilbert space. As applications, the Hardy-Littlewood theorem in infinite-dimensional Hilbert spaces and characterizations of some holomorphic function spaces related to the Bloch type space are presented.

Bounded evaluation operators from H p into q

Martin Smith (2007)

Studia Mathematica

Given 0 < p,q < ∞ and any sequence z = zₙ in the unit disc , we define an operator from functions on to sequences by T z , p ( f ) = ( 1 - | z | ² ) 1 / p f ( z ) . Necessary and sufficient conditions on zₙ are given such that T z , p maps the Hardy space H p boundedly into the sequence space q . A corresponding result for Bergman spaces is also stated.

Bounded operators on weighted spaces of holomorphic functions on the upper half-plane

Mohammad Ali Ardalani, Wolfgang Lusky (2012)

Studia Mathematica

Let v be a standard weight on the upper half-plane , i.e. v: → ]0,∞[ is continuous and satisfies v(w) = v(i Im w), w ∈ , v(it) ≥ v(is) if t ≥ s > 0 and l i m t 0 v ( i t ) = 0 . Put v₁(w) = Im wv(w), w ∈ . We characterize boundedness and surjectivity of the differentiation operator D: Hv() → Hv₁(). For example we show that D is bounded if and only if v is at most of moderate growth. We also study composition operators on Hv().

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