The algebraic size of the family of injective operators

• Autorzy: Luis Bernal-González
• Języki publikacji: EN

Abstrakty

EN

In this paper, a criterion for the existence of large linear algebras consisting, except for zero, of one-to-one operators on an infinite dimensional Banach space is provided. As a consequence, it is shown that every separable infinite dimensional Banach space supports a commutative infinitely generated free linear algebra of operators all of whose nonzero members are one-to-one. In certain cases, the assertion holds for nonseparable Banach spaces.

Słowa kluczowe

EN

One-to-one operator; Point spectrum; Algebrability; Hypercyclic operator

Kategorie tematyczne

• 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
• 47A16: Cyclic vectors, hypercyclic and chaotic operators
• 15A03: Vector spaces, linear dependence, rank
• 47L05: Linear spaces of operators

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 13-20

Daty

wydano

2017-01-01

otrzymano

2016-08-28

zaakceptowano

2016-09-08

online

2017-01-03

Twórcy

autor

Luis Bernal-González

• Departamento de Análisis Matemático. Facultad de Matemáticas Apdo. 1160. Avda. Reina Mercedes, 41080 Sevilla,

Identyfikatory

DOI

10.1515/math-2017-0005