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An invitation to operator theory
Y. Abramovich,Charalambos D. Aliprantis +1 more
- 01 Jan 2002
TL;DR: In this article, the Daugavet equation is used to describe operators on $AL$-and $AM$-spaces. But this is not the case for all operators.
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Abstract: Odds and ends Basic operator theory Operators on $AL$- and $AM$-spaces Special classes of operators Integral operators Spectral properties Some special spectra Positive matrices Irreducible operators Invariant subspaces The Daugavet equation Bibliography Index.
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Citations
The irreducibility in ordered Banach algebras
TL;DR: In this paper, it was shown that if E is a Dedekind complete Banach lattice, then the set of all order continuous elements in L(E) coincides with all positive order continuous operators on E. The spectral properties of irreducible elements in algebras with disjunctive product are investigated.
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Markov processes on Riesz spaces
TL;DR: In this paper, the authors formulate and study Markov processes in a measure-free Riesz space setting and study the convergence of these processes as well as various decomposition.
23
Deformation theory of G_2 conifolds
Spiro Karigiannis,Jason D. Lotay +1 more
TL;DR: In this article, the authors considered the deformation theory of asymptotically conical (AC) and conically singular (CS) manifolds and showed that the moduli space is smooth and its dimension in terms of topological and analytic data.
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Every operator has almost-invariant subspaces
Alexey I. Popov,Adi Tcaciuc +1 more
TL;DR: In this article, it was shown that any bounded operator on a separable, reflexive, infinite-dimensional Banach space admits a rank one perturbation which has an invariant subspace of infinite dimension and codimension.
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