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Displaying similar documents to “On Fredholm Operators and the Essential Spectrum of Singular Integral Operators.”

Spectra of partial integral operators with a kernel of three variables

Yusup Eshkabilov (2008)

Open Mathematics

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Let Ω= [a, b] × [c, d] and T 1, T 2 be partial integral operators in C (Ω): (T 1 f)(x, y) = ∫ a b k 1(x, s, y)f(s, y)ds, (T 2 f)(x, y) = ∫ c d k 2(x, ts, y)f(t, y)dt where k 1 and k 2 are continuous functions on [a, b] × Ω and Ω × [c, d], respectively. In this paper, concepts of determinants and minors of operators E−τT 1, τ ∈ ℂ and E−τT 2, τ ∈ ℂ are introduced as continuous functions on [a, b] and [c, d], respectively. Here E is the identical operator in C(Ω). In addition, Theorems on the spectra...

Note on operational quantities and Mil'man isometry spectrum.

Manuel González, Antonio Martinón (1991)

Extracta Mathematicae

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Let X and Y be infinite dimensional Banach spaces and let L(X,Y) be the class of all (linear continuous) operators acting between X and Y. Mil'man [5] introduced the isometry spectrum I(T) of T ∈ L(X,Y) in the following way: I(T) = {α ≥ 0: ∀ ε > 0, ∃M ∈ S∞(X), ∀x ∈ SM, | ||Tx|| - α | < ε}}, where S∞(X) is the set of all infinite dimensional closed subspaces of X and S...