The group of invertible elements in a Banach algebra
نویسندگان
چکیده
منابع مشابه
Some properties of Invertible Elements in Fuzzy Banach algebras
In this paper, we introduce fuzzy Banach algebra and study the properties of invertible elements and its relation with opensets. We obtain some interesting results.
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Proof. Denote by 1 the unit element of B. Let a ∈ B×. We show that 1 and a can be connected by a path in B×. Let A be the subalgebra of B generated by 1 and a. That is A = {P (a) : P (t) ∈ C[t]}. Because A× ⊂ B×, it suffices to find a path in A× that connects 1 with a. First, we determine all multiplicative functionals of A. Since A is a linear subspace of B, it is finite dimensional. Then ther...
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In [9], Dawson and the second author asked whether or not a Banach function algebra with dense invertible group can have a proper Shilov boundary. We give an example of a uniform algebra showing that this can happen, and investigate the properties of such algebras. We make some remarks on the topological stable rank of commutative, unital Banach algebras. In particular, we prove that tsr(A) ≥ t...
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We show that if T is an isometry (as metric spaces) from an open subgroup of the group of the invertible elements in a unital semisimple commutative Banach algebra onto an open subgroup of the group of the invertible elements in a unital Banach algebra, then T (1)T is an isometrical group isomorphism. In particular, T (1)T is extended to an isometrical real algebra isomorphism from A onto B.
متن کاملsome properties of invertible elements in fuzzy banach algebras
in this paper, we introduce fuzzy banach algebra and study the properties of invertible elements and its relation with opensets. we obtain some interesting results.
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1982
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-47-1-97-100