Vector space isomorphisms of non-unital reduced Banach *-algebras
Rachid ElHarti; Mohamed Mabrouk
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2015)
- Volume: 69, Issue: 2
- ISSN: 0365-1029
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topRachid ElHarti, and Mohamed Mabrouk. "Vector space isomorphisms of non-unital reduced Banach *-algebras." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 69.2 (2015): null. <http://eudml.org/doc/289795>.
@article{RachidElHarti2015,
abstract = {Let A and B be two non-unital reduced Banach *-algebras and φ: A → B be a vector space isomorphism. The two following statement holds: If φ is a *-isomorphism, then φ is isometric (with respect to the C*-norms), bipositive and φ maps some approximate identity of A onto an approximate identity of B. Conversely, any two of the later three properties imply that φ is a *-isomorphism. Finally, we show that a unital and self-adjoint spectral isometry between semi-simple Hermitian Banach algebras is an *-isomorphism.},
author = {Rachid ElHarti, Mohamed Mabrouk},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Reduced Banach algebras; preserving the spectrum.},
language = {eng},
number = {2},
pages = {null},
title = {Vector space isomorphisms of non-unital reduced Banach *-algebras},
url = {http://eudml.org/doc/289795},
volume = {69},
year = {2015},
}
TY - JOUR
AU - Rachid ElHarti
AU - Mohamed Mabrouk
TI - Vector space isomorphisms of non-unital reduced Banach *-algebras
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2015
VL - 69
IS - 2
SP - null
AB - Let A and B be two non-unital reduced Banach *-algebras and φ: A → B be a vector space isomorphism. The two following statement holds: If φ is a *-isomorphism, then φ is isometric (with respect to the C*-norms), bipositive and φ maps some approximate identity of A onto an approximate identity of B. Conversely, any two of the later three properties imply that φ is a *-isomorphism. Finally, we show that a unital and self-adjoint spectral isometry between semi-simple Hermitian Banach algebras is an *-isomorphism.
LA - eng
KW - Reduced Banach algebras; preserving the spectrum.
UR - http://eudml.org/doc/289795
ER -
References
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