摘要:

Fix a Banach latticeFand consider the following two problems. When are the order bounded operators intoFnecessarily regular? When do the regular operators intoFnecessarily form a lattice? We survey the known results in the cases that the domain is allowed to be any Banach lattice and in the case that it is restricted to be a separable Banach lattice.

ISSN:1607-3606    

DOI:10.1080/16073606.1995.9631785

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

Several non-uniform conditions sufficient for weak normal structure have recently been introduced. We show that some of these are in fact equivalent and also utilize them in applications towards a 3-space property for weak normal structure, thereby improving on earlier results.

ISSN:1607-3606    

DOI:10.1080/16073606.1995.9631786

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

We present an overview of relatively recent progress in the theory of positive operators which finds its origins in the classical spectral theory of Perron-Frobenius for positive matrices.

ISSN:1607-3606    

DOI:10.1080/16073606.1995.9631787

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

We discuss several aspects of the theory of symmetric Banach spaces of measurable operators, including their construction and certain topological and geometric properties. Particular emphasis is given to the role played by rearrangement inequalities.

ISSN:1607-3606    

DOI:10.1080/16073606.1995.9631788

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

We survey some of the extensions and ramifications of Weierstrass' theorem in the twentieth century, discussing first qualitative theory (can we approximate?) and then quantitative theory (how fast can we approximate?).

ISSN:1607-3606    

DOI:10.1080/16073606.1995.9631789

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

In this paper we present a characterization of complex lattice homomorphisms on Banach lattice algebras.

ISSN:1607-3606    

DOI:10.1080/16073606.1995.9631790

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

We extend to arbitrary semi-prime Banach algebras some results of spectral theory and Fredholm theory obtained in [1] and [2] for multipliers defined in commutative semi-simple Banach algebras.

ISSN:1607-3606    

DOI:10.1080/16073606.1995.9631791

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

LetAbe a von Neumann algebra on a Hilbert spaceHand letP(A) denote the projections ofA. A comparative probability (CP) onA(or more correctly onP(A)) is a preorder ⪯ onP(A) satisfying:

ISSN:1607-3606    

DOI:10.1080/16073606.1995.9631792

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

Since 1970 a number of operational quantities, characteristic of either the semi-Fredholm operators or of some “ideal” of compact-like operators, have been introduced in the theory of bounded operators between Banach spaces and applied successfully to for example perturbation theory. More recently such quantities have been introduced even in the abstract setting of Fredholm theory in a von Neumann algebra relative to some closed two-sided ideal. We show that in this fairly general setting there is only one “reasonable” set of such quantities—a result which in its present form is to the best of our knowledge new even in the case ofB(H), the algebra of all bounded operators on a Hilbert spaceH.We accomplish this by first of all introducing the concept of a (reduced) minimum modulus in the setting of C*-algebras and developing the relevant techniques. In the process we generalise a result of Nikaido [N].

ISSN:1607-3606    

DOI:10.1080/16073606.1995.9631793

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

Throughout the literature on optimal control in Banach spaces, hypotheses like “separable and reflexive” are frequently encountered. In this note we consider one such case, studied by Peichl and Schappacher. Using techniques from Banach space theory and the theory of vector measures, we show how to remove the hypothesis of reflexivity and translate the problem of controls to one about the strong continuity of an adjoint semigroup on the positive real axis.

ISSN:1607-3606    

DOI:10.1080/16073606.1995.9631794

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor