Foundations of the Fredholm Alternative Theorem, Equicontinuous Operators and Completely Continuous Operators
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چکیده
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Comments on completely continuous operators and Fredholm determinants
Completely continuous operators Let A be a Banach algebra with |A| % {1}, where A := {a ∈ A : |ab| = |a| |b| for all b ∈ A} is the set of all multiplicative units in A (equivalently, A = {a ∈ A : |a| |a| = 1}). Then for any Banach modules M,N over A, an A-linear map L : M → N is continuous iff supm6=0 |L(m)| |m| < ∞. Let BA(M,N) be the space of such maps. With the norm |L| := supm6=0 |L(m)| |m|...
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ژورنال
عنوان ژورنال: BIBECHANA
سال: 1970
ISSN: 2382-5340,2091-0762
DOI: 10.3126/bibechana.v8i0.5700