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About 10,000 papers for “linear operators”

Linear Operators

Theodore V. Hromadka, Chung‐Cheng Yen, George F. Pinder · Lecture notes in engineering · 1987

Cited by 0

Linear Operators

William L. Dunn, J. Kenneth Shultis · Elsevier eBooks · 2022

Cited by 0

Linear Operators

I. V. Kolokolov, E. A. Kuznetsov, A. I. Milstein et al. · 2024

Cited by 0

Linear Operators

Vijay Kumar Malhotra · University of North Texas Digital Library (University of North Texas) · 1975

This paper is a study of linear operators defined on normed linear spaces. A basic knowledge of set theory and vector spaces is assumed, and all spaces considered have real vector spaces. The first chapter is a general introduction that contains assumed definitions and theorems. Included in this chapter is material concerning linear functionals, continuity, and boundedness. The second chapter contains the proofs of three fundamental theorems of linear analysis: the Open Mapping Theorem, the Hahn-Banach Theorem, and the Uniform Boundedness Principle. The third chapter is concerned with applying some of the results established in earlier chapters. In particular, the concepts of compact operators and Schauder bases are introduced, and a proof that an operator is compact if and only if its adjoint is compact is included. This chapter concludes with a proof of an important application of the Open Mapping Theorem, namely, the Closed Graph Theorem.

Cited by 0Open access

Linear operators

Victor Khatskevich, David Shoiykhet · Birkhäuser Basel eBooks · 1994

This chapter, as well as Chapter 0, is mainly auxiliary. However, compared with Chapter 0, the topics considered here are more special. Some of the subsequent results were presented only in research papers, but not in monographs. Therefore, our exposition in this chapter will be quite detailed, and will include proofs.

Cited by 0

Linear operators

Omori, Hideki · Translations of mathematical monographs · 2016

Cited by 0

Linear operators

E. Vinberg · Graduate studies in mathematics · 2003

Cited by 0Open access

Linear operators

Dunford, Nelson, Schwartz, Jacob T · CERN Document Server (European Organization for Nuclear Research)

Cited by 0

Linear Operators

Peter Petersen · Undergraduate texts in mathematics · 2012

Cited by 0

Linear operators

Dunford, Nelson., Schwartz, Jacob T., joint author. · The Journal of the Abraham Lincoln Association

Cited by 0Open access

Linear operators

Martin Schechter · Graduate studies in mathematics · 2001

Cited by 0

Linear Operators

Larisa Beilina, Evgenii M. Karchevskii, М. M. Карчевский · 2017

Cited by 0

Linear Operators

Malhotra, Vijay Kumar · University of North Texas Digital Library (University of North Texas) · 1975

This paper is a study of linear operators defined on normed linear spaces. A basic knowledge of set theory and vector spaces is assumed, and all spaces considered have real vector spaces. The first chapter is a general introduction that contains assumed definitions and theorems. Included in this chapter is material concerning linear functionals, continuity, and boundedness. The second chapter contains the proofs of three fundamental theorems of linear analysis: the Open Mapping Theorem, the Hahn-Banach Theorem, and the Uniform Boundedness Principle. The third chapter is concerned with applying some of the results established in earlier chapters. In particular, the concepts of compact operators and Schauder bases are introduced, and a proof that an operator is compact if and only if its adjoint is compact is included. This chapter concludes with a proof of an important application of the Open Mapping Theorem, namely, the Closed Graph Theorem.

Cited by 0Open access

Linear operators

Dunford, Nelson., Schwartz, Jacob T. · The Journal of the Abraham Lincoln Association

Cited by 0Open access

Continuity of linear operators commuting with continuous linear operators

B. E. Johnson · Transactions of the American Mathematical Society · 1967

1. Introduction. In [6] and [8] we showed that centralisers (that is operators commuting with multiplication) on certain Banach algebras are necessarily continuous. In the present paper we consider whether an operator on a Banach space commuting with a continuous or a closed operator must itself be continuous. We also consider the more general problem of whether an operator S; E1 -- E2, satisfying ST1 = T2S, with T1, T2 continuous, must be continuous. If the operators T1, T2 are operators of scalar type [3, p. 226] or operators in BK spaces [15, p. 29] given by triangular matrices, we see that the only discontinuous S are the obvious ones. In ?8 we consider operators in L1(-oo, + oo) and le(-oo, + oo) commuting with the translation operator (Tf)(x) =f(x + 1). For the L1 space any operator commuting with T is continuous, whereas in W6(-oo, +oo) we can find a discontinuous operator commuting with all the translation operators. A full solution to this problem might be useful in discussing the extent to which discontinuous homomorphisms between Banach algebras exist since if 0 is a homomorphism it satisfies f(ab)=0(a)0(b) which can be written ?bLa=L<(a) where LaX = ax. 2. Discontinuous commutants. The Banach-Steinhaus theorem [2, p. 27] makes it necessary to employ transfinite methods to construct discontinuous operators in Banach spaces. Thus it can be difficult, when considering whether there are discontinuous operators satisfying certain conditions, to show that the answer is affirmative. We consider two cases in which the construction is simple. First, however, some notation.

Cited by 52Open access