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Ideal norms and trigonometric orthonormal systems

Jörg Wenzel (1994)

Studia Mathematica

We characterize the UMD-property of a Banach space X by sequences of ideal norms associated with trigonometric orthonormal systems. The asymptotic behavior of those numerical parameters can be used to decide whether X is a UMD-space. Moreover, if this is not the case, we obtain a measure that shows how far X is from being a UMD-space. The main result is that all described sequences are not only simultaneously bounded but are also asymptotically equivalent.

Ideals and hereditary subalgebras in operator algebras

Melahat Almus, David P. Blecher, Charles John Read (2012)

Studia Mathematica

This paper may be viewed as having two aims. First, we continue our study of algebras of operators on a Hilbert space which have a contractive approximate identity, this time from a more Banach-algebraic point of view. Namely, we mainly investigate topics concerned with the ideal structure, and hereditary subalgebras (or HSA's, which are in some sense a generalization of ideals). Second, we study properties of operator algebras which are hereditary subalgebras in their bidual, or equivalently which...

Ideals of extendable and liftable operators.

Pawel Domanski (2003)

RACSAM

Se introducen los ideales de operadores que admiten extensión o levantamiento y se presenta una nueva aproximación al estudio de la escisión de sucesiones exactas cortas de espacios de Banach. Se considera la maximalidad de estos ideales y se investiga si son cerrados respecto de los límites puntuales acotados. Se resumen algunos ejemplos y se clarifica el papel de los espacios L1 y L∞.

Ideals of homogeneous polynomials and weakly compact approximation property in Banach spaces

Erhan Çalışkan (2007)

Czechoslovak Mathematical Journal

We show that a Banach space E has the weakly compact approximation property if and only if each continuous Banach-valued polynomial on E can be uniformly approximated on compact sets by homogeneous polynomials which are members of the ideal of homogeneous polynomials generated by weakly compact linear operators. An analogous result is established also for the compact approximation property.

Idéaux fermés de certaines algèbres de Beurling et application aux opérateurs à spectre dénombrable

Cyril Agrafeuil (2005)

Studia Mathematica

We denote by the unit circle and by the unit disc of ℂ. Let s be a non-negative real and ω a weight such that ω ( n ) = ( 1 + n ) s (n ≥ 0) and the sequence ( ω ( - n ) / ( 1 + n ) s ) n ≥ 0 is non-decreasing. We define the Banach algebra A ω ( ) = f ∈ ( ) : | | f | | ω = ∑ n = - ∞ + ∞ | f ̂ ( n ) | ω ( n ) < + ∞ . If I is a closed ideal of A ω ( ) , we set h ⁰ ( I ) = z ∈ : f ( z ) = 0 ( f ∈ I ) . We describe all closed ideals I of A ω ( ) such that h⁰(I) is at most countable. A similar result is obtained for closed ideals of the algebra A ⁺ s ( ) = f ∈ A ω ( ) : f ̂ ( n ) = 0 ( n < 0 ) without inner factor. Then we use this description to establish a link between operators with countable spectrum and interpolating sets...

Identification problems for degenerate parabolic equations

Fadi Awawdeh, Hamed M. Obiedat (2013)

Applications of Mathematics

This paper deals with multivalued identification problems for parabolic equations. The problem consists of recovering a source term from the knowledge of an additional observation of the solution by exploiting some accessible measurements. Semigroup approach and perturbation theory for linear operators are used to treat the solvability in the strong sense of the problem. As an important application we derive the corresponding existence, uniqueness, and continuous dependence results for different...

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