Pure States and P-Commutative Banach *-Algebras.
R.S. Doran, Wayne Tiller (1988)
Manuscripta mathematica
Similarity:
R.S. Doran, Wayne Tiller (1988)
Manuscripta mathematica
Similarity:
W. Żelazko (1969)
Colloquium Mathematicae
Similarity:
Bruno Iochum, Guy Loupias (1991)
Annales scientifiques de l'Université de Clermont. Mathématiques
Similarity:
Joel F. Feinstein, Herbert Kamowitz (2010)
Banach Center Publications
Similarity:
This paper is a continuation of our study of compact, power compact, Riesz, and quasicompact endomorphisms of commutative Banach algebras. Previously it has been shown that if B is a unital commutative semisimple Banach algebra with connected character space, and T is a unital endomorphism of B, then T is quasicompact if and only if the operators Tⁿ converge in operator norm to a rank-one unital endomorphism of B. In this note the discussion is extended in two ways: we discuss endomorphisms...
Donald Z. Spicer (1973)
Colloquium Mathematicae
Similarity:
V. Müller (1982)
Studia Mathematica
Similarity:
Sommariva, Alvise, Vianello, Marco (2001)
Journal of Inequalities and Applications [electronic only]
Similarity:
Ignacio Zalduendo (1991)
Publicacions Matemàtiques
Similarity:
A simple and natural example is given of a non-commuting Arens multiplication.
Antonio Fernández López, Eulalia García Rus (1986)
Extracta Mathematicae
Similarity:
C. J. Read (2005)
Studia Mathematica
Similarity:
It is a long standing open problem whether there is any infinite-dimensional commutative Banach algebra without nontrivial closed ideals. This is in some sense the Banach algebraists' counterpart to the invariant subspace problem for Banach spaces. We do not here solve this famous problem, but solve a related problem, that of finding (necessarily commutative) infinite-dimensional normed algebras which do not even have nontrivial closed subalgebras. Our examples are incomplete normed...
Osamu Hatori, Go Hirasawa, Takeshi Miura (2010)
Open Mathematics
Similarity:
Let A and B be unital, semisimple commutative Banach algebras with the maximal ideal spaces M A and M B, respectively, and let r(a) be the spectral radius of a. We show that if T: A → B is a surjective mapping, not assumed to be linear, satisfying r(T(a) + T(b)) = r(a + b) for all a; b ∈ A, then there exist a homeomorphism φ: M B → M A and a closed and open subset K of M B such that for all a ∈ A, where e is unit element of A. If, in addition, and on M B, then T is an algebra isomorphism. ...
P. A. Dabhi, H. V. Dedania (2009)
Studia Mathematica
Similarity:
We prove that a semisimple, commutative Banach algebra has either exactly one uniform norm or infinitely many uniform norms; this answers a question asked by S. J. Bhatt and H. V. Dedania [Studia Math. 160 (2004)]. A similar result is proved for C*-norms on *-semisimple, commutative Banach *-algebras. These properties are preserved if the identity is adjoined. We also show that a commutative Beurling *-algebra L¹(G,ω) has exactly one uniform norm if and only if it has exactly one C*-norm;...
Tewari, U.B., Dutta, M., Madan, Shobha (1982)
International Journal of Mathematics and Mathematical Sciences
Similarity:
Rachid ElHarti, Mohamed Mabrouk (2015)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
Similarity:
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...
E. Kaniuth, A. T. Lau, A. Ülger (2007)
Studia Mathematica
Similarity:
Let A and B be semisimple commutative Banach algebras with bounded approximate identities. We investigate the problem of extending a homomorphism φ: A → B to a homomorphism of the multiplier algebras M(A) and M(B) of A and B, respectively. Various sufficient conditions in terms of B (or B and φ) are given that allow the construction of such extensions. We exhibit a number of classes of Banach algebras to which these criteria apply. In addition, we prove a polar decomposition for homomorphisms...
Katsylo, Pavel, Mikhailov, Dmitry (1997)
Journal of Lie Theory
Similarity: