The algebraic size of the family of injective operators

Luis 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 -