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- W2044379140 abstract "We consider an arbitrary commutative Banach algebra over the complex numbers. Let B denote the algebra, {a, b, c, x, y, z, * * } its elements, and {X, IA, v, . } complex numbers. We assume that B contains a unit element, e, with l|ell = 1. If a-1 exists (aa-1 = a-la = e), the element a is called regular. The set of regular elements will be denoted by G. It is well known that (1) G is a topological group relative to multiplication and (2) G is an open subset of B. Since G is open, it is a union of maximal open connected sets, its components. We call the G1 containing the unit e the principal component [1]. It is easy to see that G1 is a subgroup of G. The function exp (x)_ e + 1 xn/n! is defined for all x in B and has the usual properties of the classical exponential function. If we let 7r-(Gi) denote the fundamental group of G1, we may state our main result as follows:" @default.
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- W2044379140 title "The fundamental group of the principal component of a commutative Banach algebra" @default.
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