Bounded elements and spectrum in Banach quasi $^*$-algebras
Studia Mathematica, Tome 172 (2006) no. 3, pp. 249-273
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
A normal Banach quasi $^*$-algebra
$({\mathfrak X},)$ has a distinguished Banach $^*$-algebra ${\mathfrak X}_{\rm b}$ consisting
of {bounded} elements of ${\mathfrak X}$. The latter $^*$-algebra is
shown to coincide with the set of elements of ${\mathfrak X}$ having finite
spectral radius. If the family ${\cal P}({\mathfrak X})$ of bounded
invariant positive sesquilinear forms on ${\mathfrak X}$ contains
sufficiently many elements then the Banach $^*$-algebra of bounded
elements can be characterized via a $C^*$-seminorm defined by the
elements of ${\cal P}({\mathfrak X})$.
Keywords:
normal banach quasi * algebra mathfrak has distinguished banach * algebra mathfrak consisting bounded elements mathfrak latter * algebra shown coincide set elements mathfrak having finite spectral radius family cal mathfrak bounded invariant positive sesquilinear forms mathfrak contains sufficiently many elements banach * algebra bounded elements characterized via * seminorm defined elements cal mathfrak
Affiliations des auteurs :
Camillo Trapani 1
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author = {Camillo Trapani},
title = {Bounded elements and spectrum in {Banach} quasi $^*$-algebras},
journal = {Studia Mathematica},
pages = {249--273},
publisher = {mathdoc},
volume = {172},
number = {3},
year = {2006},
doi = {10.4064/sm172-3-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm172-3-4/}
}
Camillo Trapani. Bounded elements and spectrum in Banach quasi $^*$-algebras. Studia Mathematica, Tome 172 (2006) no. 3, pp. 249-273. doi: 10.4064/sm172-3-4
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