On the o-Spectrum of Order Bounded Operators.
Helmut H. Schaefer (1977)
Mathematische Zeitschrift
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Helmut H. Schaefer (1977)
Mathematische Zeitschrift
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Gh. Constantin (1975)
Matematički Vesnik
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Derek Kitson (2009)
Studia Mathematica
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We extend the notion of ascent and descent for an operator acting on a vector space to sets of operators. If the ascent and descent of a set are both finite then they must be equal and give rise to a canonical decomposition of the space. Algebras of operators, unions of sets and closures of sets are treated. As an application we construct a Browder joint spectrum for commuting tuples of bounded operators which is compact-valued and has the projection property.
Albert Schneider, Frank Mantlik (1990)
Mathematische Zeitschrift
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Johann Walter (1972)
Mathematische Zeitschrift
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Bucur, Amelia (1996)
General Mathematics
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Benharrat, Mohammed, Messirdi, Bekkai (2011)
Serdica Mathematical Journal
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2010 Mathematics Subject Classification: 47A10. We show that the symmetric difference between the generalized Kato spectrum and the essential spectrum defined in [7] by sec(T) = {l О C ; R(lI-T) is not closed } is at most countable and we also give some relationship between this spectrum and the SVEP theory.
Marcin Bownik, John Jasper (2015)
Bulletin of the Polish Academy of Sciences. Mathematics
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Given a finite set X⊆ ℝ we characterize the diagonals of self-adjoint operators with spectrum X. Our result extends the Schur-Horn theorem from a finite-dimensional setting to an infinite-dimensional Hilbert space analogous to Kadison's theorem for orthogonal projections (2002) and the second author's result for operators with three-point spectrum (2013).
Djordjević, Slaviša V. (1997)
Matematichki Vesnik
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Takeshi Miura, Dai Honma (2009)
Open Mathematics
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Let A and B be standard operator algebras on Banach spaces X and Y, respectively. The peripheral spectrum σπ (T) of T is defined by σπ (T) = z ∈ σ(T): |z| = maxw∈σ(T) |w|. If surjective (not necessarily linear nor continuous) maps φ, ϕ: A → B satisfy σπ (φ(S)ϕ(T)) = σπ (ST) for all S; T ∈ A, then φ and ϕ are either of the form φ(T) = A 1 TA 2 −1 and ϕ(T) = A 2 TA 1 −1 for some bijective bounded linear operators A 1; A 2 of X onto Y, or of the form φ(T) = B 1 T*B 2 −1 and ϕ(T) = B 2 T*B...
John Piepenbrink (1974)
Mathematische Zeitschrift
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Andrzej Sołtysiak (1989)
Colloquium Mathematicae
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V. Rakočević (1985)
Matematički Vesnik
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J.I. NIETO (1968)
Mathematische Annalen
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