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Nevanlinna algebras

A. Haldimann, H. Jarchow (2001)

Studia Mathematica

The Nevanlinna algebras, α p , of this paper are the L p variants of classical weighted area Nevanlinna classes of analytic functions on = z ∈ ℂ: |z| < 1. They are F-algebras, neither locally bounded nor locally convex, with a rich duality structure. For s = (α+2)/p, the algebra F s of analytic functions f: → ℂ such that ( 1 - | z | ) s | f ( z ) | 0 as |z| → 1 is the Fréchet envelope of α p . The corresponding algebra s of analytic f: → ℂ such that s u p z ( 1 - | z | ) s | f ( z ) | < is a complete metric space but fails to be a topological vector space. F s is also...

New criteria for boundedness and compactness of weighted composition operators mapping into the Bloch space

Flavia Colonna (2013)

Open Mathematics

Let ψ and φ be analytic functions on the open unit disk 𝔻 with φ( 𝔻 ) ⊆ 𝔻 . We give new characterizations of the bounded and compact weighted composition operators W ψ,ϕ from the Hardy spaces H p, 1 ≤ p ≤ ∞, the Bloch space B, the weighted Bergman spaces A αp, α > − 1,1 ≤ p < ∞, and the Dirichlet space 𝒟 to the Bloch space in terms of boundedness (respectively, convergence to 0) of the Bloch norms of W ψ,ϕ f for suitable collections of functions f in the respective spaces. We also obtain characterizations...

Nonatomic Lipschitz spaces

Nik Weaver (1995)

Studia Mathematica

We abstractly characterize Lipschitz spaces in terms of having a lattice-complete unit ball and a separating family of pure normal states. We then formulate a notion of "measurable metric space" and characterize the corresponding Lipschitz spaces in terms of having a lattice complete unit ball and a separating family of normal states.

Normal bases for the space of continuous functions defined on a subset of Zp.

Ann Verdoodt (1994)

Publicacions Matemàtiques

Let K be a non-archimedean valued field which contains Qp and suppose that K is complete for the valuation |·|, which extends the p-adic valuation. Vq is the closure of the set {aqn|n = 0,1,2,...} where a and q are two units of Zp, q not a root of unity. C(Vq → K) is the Banach space of continuous functions from Vq to K, equipped with the supremum norm. Our aim is to find normal bases (rn(x)) for C(Vq → K), where rn(x) does not have to be a polynomial.

Notes on interpolation of Hardy spaces

Quanhua Xu (1992)

Annales de l'institut Fourier

Let H p denote the usual Hardy space of analytic functions on the unit disc ( 0 &lt; p ) . We prove that for every function f H 1 there exists a linear operator T defined on L 1 ( T ) which is simultaneously bounded from L 1 ( T ) to H 1 and from L ( T ) to H such that T ( f ) = f . Consequently, we get the following results ( 1 p 0 , p 1 ) :1) ( H p 0 , H p 1 ) is a Calderon-Mitjagin couple;2) for any interpolation functor F , we have F ( H p 0 , H p 1 ) = H ( F ( L p 0 ( T ) , L p 1 ( T ) ) ) , where H ( F ( L p 0 ( T ) , L p 1 ( T ) ) ) denotes the closed subspace of F ( L p 0 ( T ) , L p 1 ( T ) ) of all functions whose Fourier coefficients vanish on negative integers.These results also extend to Hardy...

Numerical index with respect to an operator

Mohammad Ali Ardalani (2014)

Studia Mathematica

We introduce new concepts of numerical range and numerical radius of one operator with respect to another one, which generalize in a natural way the known concepts of numerical range and numerical radius. We study basic properties of these new concepts and present some examples.

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