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We deal with the algebras consisting of the quotients that produce bounded evaluation on suitable ideals of the multiplication algebra of a normed semiprime algebra A. These algebras of quotients, which contain A, are subalgebras of the bounded algebras of quotients of A, and they have an algebra seminorm for which the relevant inclusions are continuous. We compute these algebras of quotients for some norm ideals on a Hilbert space H: 1) the algebras of quotients with bounded evaluation of the ideal...
A linear subspace M of a Jordan algebra J is said to be a Lie triple ideal of J if [M,J,J] ⊆ M, where [·,·,·] denotes the associator. We show that every Lie triple ideal M of a nondegenerate Jordan algebra J is either contained in the center of J or contains the nonzero Lie triple ideal [U,J,J], where U is the ideal of J generated by [M,M,M].
Let H be a Jordan algebra, let J be a prime nondegenerate Jordan algebra with extended centroid C and unital central closure Ĵ, and let...
We establish interpolation properties under limiting real methods for a class of closed ideals including weakly compact operators, Banach-Saks operators, Rosenthal operators and Asplund operators. We show that they behave much better than compact operators.
We review several results on interpolation of Banach algebras and factorization of weakly compact homomorphisms. We also establish a new result on interpolation of multilinear operators.
We prove that there exists a real or complex central simple associative algebra M with minimal one-sided ideals such that, for every non-Jordan associative polynomial p, a Jordan-algebra norm can be given on M in such a way that the action of p on M becomes discontinuous.
The paper establishes necessary and sufficient conditions for compactness of operators acting between general K-spaces, general J-spaces and operators acting from a J-space into a K-space. Applications to interpolation of compact operators are also given.
This note deals with interpolation methods defined by means of polygons. We show necessary and sufficient conditions for compactness of operators acting from a J-space into a K-space.
We investigate inclusion indices for quasi-Banach spaces. First we consider the case of function spaces on , then the sequence case and finally we develop an abstract approach dealing with indices defined by the real interpolation scale gen- erated by a quasi-Banach couple.
This paper deals with the following problem:
Let T be a given operator. Find conditions on v(x) (resp. u(x)) such that
∫ |Tf(x)|pu(x) dx ≤ C ∫ |f(x)|pv(x) dx
is satisfied for some u(x) (resp. v(x)).
Using vector-valued inequalities the problem is solved for: Carleson's maximal operator of Fourier partial sums, Littlewood-Paley square functions, Hilbert transform of functions valued in...
Here are given the figures of this paper, initially published with some omissions.
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