# The algebraic size of the family of injective operators

Open Mathematics (2017)

- Volume: 15, Issue: 1, page 13-20
- ISSN: 2391-5455

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topLuis Bernal-González. "The algebraic size of the family of injective operators." Open Mathematics 15.1 (2017): 13-20. <http://eudml.org/doc/288018>.

@article{LuisBernal2017,

abstract = {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.},

author = {Luis Bernal-González},

journal = {Open Mathematics},

keywords = {One-to-one operator; Point spectrum; Algebrability; Hypercyclic operator},

language = {eng},

number = {1},

pages = {13-20},

title = {The algebraic size of the family of injective operators},

url = {http://eudml.org/doc/288018},

volume = {15},

year = {2017},

}

TY - JOUR

AU - Luis Bernal-González

TI - The algebraic size of the family of injective operators

JO - Open Mathematics

PY - 2017

VL - 15

IS - 1

SP - 13

EP - 20

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/288018

ER -

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