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Decomposable subspaces of Banach spaces.

Manuel González, Antonio Martinón (2003)

RACSAM

We introduce and study the notion of hereditarily A-indecomposable Banach space for A a space ideal. For a hereditarily A-indecomposable space X we show that the operators from X into a Banach space Y can be written as the union of two sets A Φ+(X,Y) and A(X;Y ). For some ideals A defined in terms of incomparability, the first set is open, the second set correspond to a closed operator ideal and the union is disjoint.

Decomposing and twisting bisectorial operators

Wolfgang Arendt, Alessandro Zamboni (2010)

Studia Mathematica

Bisectorial operators play an important role since exactly these operators lead to a well-posed equation u'(t) = Au(t) on the entire line. The simplest example of a bisectorial operator A is obtained by taking the direct sum of an invertible generator of a bounded holomorphic semigroup and the negative of such an operator. Our main result shows that each bisectorial operator A is of this form, if we allow a more general notion of direct sum defined by an unbounded closed projection. As a consequence...

Decomposition and disintegration of positive definite kernels on convex *-semigroups

Jan Stochel (1992)

Annales Polonici Mathematici

The paper deals with operator-valued positive definite kernels on a convex *-semigroup whose Kolmogorov-Aronszajn type factorizations induce *-semigroups of bounded shift operators. Any such kernel Φ has a canonical decomposition into a degenerate and a nondegenerate part. In case is commutative, Φ can be disintegrated with respect to some tight positive operator-valued measure defined on the characters of if and only if Φ is nondegenerate. It is proved that a representing measure of a positive...

Décomposition atomique des espaces de Bergman.

Frédéric Symesak (1995)

Publicacions Matemàtiques

The aim of this paper is to establish the theorem of atomic decomposition of weighted Bergman spaces Ap(Ω), where Ω is a domain of finite type in C2. We construct a kernel function H(z,w) which is a reproducing kernel for Ap(Ω) and we prove that the associated integral operator H is bounded in Lp(Ω).

Decomposition of operators with countable spectrum.

Lucas Jódar (1986)

Stochastica

Sufficient spectral conditions for the existence of a spectral decomposition of an operator T defined on a Banach space X, with countable spectrum, are given. We apply the results to obtain the West decomposition of certain Riesz operators.

Decompositions and asymptotic limit for bicontractions

Marek Kosiek, Laurian Suciu (2012)

Annales Polonici Mathematici

The asymptotic limit of a bicontraction T (that is, a pair of commuting contractions) on a Hilbert space is used to describe a Nagy-Foiaş-Langer type decomposition of T. This decomposition is refined in the case when the asymptotic limit of T is an orthogonal projection. The case of a bicontraction T consisting of hyponormal (even quasinormal) contractions is also considered, where we have S T * = S ² T * .

Decompositions for real Banach spaces with small spaces of operators

Manuel González, José M. Herrera (2007)

Studia Mathematica

We consider real Banach spaces X for which the quotient algebra (X)/ℐn(X) is finite-dimensional, where ℐn(X) stands for the ideal of inessential operators on X. We show that these spaces admit a decomposition as a finite direct sum of indecomposable subspaces X i for which ( X i ) / ℐ n ( X i ) is isomorphic as a real algebra to either the real numbers ℝ, the complex numbers ℂ, or the quaternion numbers ℍ. Moreover, the set of subspaces X i can be divided into subsets in such a way that if X i and X j are in different subsets,...

Decompositions of Beurling type for E₀-semigroups

Rolf Gohm (2006)

Banach Center Publications

We define tensor product decompositions of E₀-semigroups with a structure analogous to a classical theorem of Beurling. Such decompositions can be characterized by adaptedness and exactness of unitary cocycles. For CCR-flows we show that such cocycles are convergent.

Deformation quantization and Borel's theorem in locally convex spaces

Miroslav Engliš, Jari Taskinen (2007)

Studia Mathematica

It is well known that one can often construct a star-product by expanding the product of two Toeplitz operators asymptotically into a series of other Toeplitz operators multiplied by increasing powers of the Planck constant h. This is the Berezin-Toeplitz quantization. We show that one can obtain in a similar way in fact any star-product which is equivalent to the Berezin-Toeplitz star-product, by using instead of Toeplitz operators other suitable mappings from compactly supported smooth functions...

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