Displaying similar documents to “A note on spaces of type H ∞ + C ”

Operators on spaces of analytic functions

K. Seddighi (1994)

Studia Mathematica

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Let M z be the operator of multiplication by z on a Banach space of functions analytic on a plane domain G. We say that M z is polynomially bounded if ∥ M p ∥ ≤ C ∥ p ∥ G for every polynomial p. We give necessary and sufficient conditions for M z to be polynomially bounded. We also characterize the finite-codimensional invariant subspaces and derive some spectral properties of the multiplication operator in case the underlying space is Hilbert.

Operators determining the complete norm topology of C(K)

A. Villena (1997)

Studia Mathematica

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For any uniformly closed subalgebra A of C(K) for a compact Hausdorff space K without isolated points and x 0 ∈ A , we show that every complete norm on A which makes continuous the multiplication by x 0 is equivalent to ∥ · ∥ ∞ provided that x 0 - 1 ( λ ) has no interior points whenever λ lies in ℂ. Actually, these assertions are equivalent if A = C(K).

Spaces of type H ∞ + C

Walter Rudin (1975)

Annales de l'institut Fourier

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A simple theorem is proved which states a sufficient condition for the sum ot two closed subspaces of a Banach space to be closed. This leads to several analogues of Sarason’s theorem which states that H ∞ + C is a closed subalgebra of L ∞ . In these analogues, the unit circle is replaces by other groups, and the unit disc is replaced by polydiscs or by balls in spaces of several complex variables. Sums of closed ideals in Banach algebras are also studied.

On inessential and improjective operators.

Pietro Aiena, Manuel González (1998)

Studia Mathematica

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We give several characterizations of the improjective operators, introduced by Tarafdar, and we characterize the inessential operators among the improjective operators. It is an interesting problem whether both classes of operators coincide in general. A positive answer would provide, for example, an intrinsic characterization of the inessential operators. We give several equivalent formulations of this problem and we show that the inessential operators acting between certain pairs of...