Invariance of spectrum for representations of $\mathrm {C}*$-algebras on Banach spaces
نویسندگان
چکیده
منابع مشابه
Invariance of Spectrum for Representations of C∗-algebras on Banach Spaces
Let K be a Banach space, B a unital C∗-algebra, and π : B → L(K) an injective, unital homomorphism. Suppose that there exists a function γ : K×K → R+ such that, for all k, k1, k2 ∈ K, and all b ∈ B, (a) γ(k, k) = ‖k‖2, (b) γ(k1, k2) ≤ ‖k1‖ ‖k2‖, (c) γ(πbk1, k2) = γ(k1, πb∗k2). Then for all b ∈ B, the spectrum of b in B equals the spectrum of πb as a bounded linear operator on K. If γ satisfies ...
متن کاملamenability of banach algebras
chapters 1 and 2 establish the basic theory of amenability of topological groups and amenability of banach algebras. also we prove that. if g is a topological group, then r (wluc (g)) (resp. r (luc (g))) if and only if there exists a mean m on wluc (g) (resp. luc (g)) such that for every wluc (g) (resp. every luc (g)) and every element d of a dense subset d od g, m (r)m (f) holds. chapter 3 inv...
15 صفحه اولthe structure of lie derivations on c*-algebras
نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.
15 صفحه اولRepresentations of Compact Groups on Banach Algebras
Let a compact group U act by automorphisms of a commutative regular and Wiener Banach algebra A. We study representations Ru of U on quotient spaces A/I(üj), where u> is an orbit of U in the Gelfand space X of A and L(uj) is the minimal closed ideal with hull w C X. The main result of the paper is: if A = AP(X) is a weighted Fourier algebra on a LCA group X = A with a subpolynomial weight p on ...
متن کاملSpectrum Preserving Linear Maps Between Banach Algebras
In this paper we show that if A is a unital Banach algebra and B is a purely innite C*-algebra such that has a non-zero commutative maximal ideal and $phi:A rightarrow B$ is a unital surjective spectrum preserving linear map. Then $phi$ is a Jordan homomorphism.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1997
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-97-03536-3