Axiomatic etal maps and a theory of spectrum

Axiomatic theory of spectrum III. — Semiregularities

The notion of regularity in a Banach algebra was introduced and studied in [KM] and [MM]. A non-empty subset R of a unital Banach algebra A is called a regularity if it satisfies the following two conditions: (i) if a ∈ A and n ∈ N, then a ∈ R ⇔ a ∈ R, (ii) if a, b, c, d are mutually commuting elements of A satisfying ac + bd = 1A then ab ∈ R ⇔ a, b ∈ R. The axioms of regularities are weak enou...

A Survey of Invertibility and Spectrum Preserving Linear Maps

Axiomatic domain theory in categories of partial maps

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Corrigendum an Addendum : “ On the axiomatic theory of spectrum II ”

Recall some notations and terminology from [4]. For closed subspaces M, L of a Banach space X we write M e ⊂L (M is essentially contained in L ) if there exists a finite-dimensional subspace F ⊂ X such that M ⊂ L + F . Equivalently, dim M/(M ∩L) = dim(M + L)/L < ∞. Similarly we write M e =L if M e ⊂L and L e ⊂M . For a (bounded linear) operator T ∈ L(X) write R∞(T ) = ∞n=0 R(T) and N∞(T ) = ⋃∞ ...

a survey of invertibility and spectrum preserving linear maps