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.
@article{bwmeta1.element.doi-10_1515_math-2017-0005,
author = {Luis Bernal-Gonz\'alez},
title = {The algebraic size of the family of injective operators},
journal = {Open Mathematics},
volume = {15},
year = {2017},
pages = {13-20},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2017-0005}
}
Luis Bernal-González. The algebraic size of the family of injective operators. Open Mathematics, Tome 15 (2017) pp. 13-20. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2017-0005/