On operators with the same spectrum
Gh. Constantin (1975)
Matematički Vesnik
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Gh. Constantin (1975)
Matematički Vesnik
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J. Janas (1988)
Colloquium Mathematicae
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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.
Schôichi Ôta, Franciszek Hugon Szafraniec (2004)
Studia Mathematica
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The paper concerns operators of deformed structure like q-normal and q-hyponormal operators with the deformation parameter q being a positive number different from 1. In particular, an example of a q-hyponormal operator with empty spectrum is given, and q-hyponormality is characterized in terms of some operator inequalities.
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).
Chun Guang Li, Ting Ting Zhou (2014)
Studia Mathematica
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A bounded linear operator T acting on a Hilbert space is said to be polaroid if each isolated point in the spectrum is a pole of the resolvent of T. There are several generalizations of the polaroid property. We investigate compact perturbations of polaroid type operators. We prove that, given an operator T and ε > 0, there exists a compact operator K with ||K|| < ε such that T + K is polaroid. Moreover, we characterize those operators for which a certain polaroid type property...
Bucur, Amelia (1996)
General Mathematics
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Mohammed Hichem Mortad (2011)
Colloquium Mathematicae
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We present a new approach to the question of when the commutativity of operator exponentials implies that of the operators. This is proved in the setting of bounded normal operators on a complex Hilbert space. The proofs are based on some results on similarities by Berberian and Embry as well as the celebrated Fuglede theorem.
Lutz W. Weis (1986)
Extracta Mathematicae
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Aicha Chaban, Mohammed Hichem Mortad (2013)
Colloquium Mathematicae
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The present paper is mainly concerned with equations involving exponentials of bounded normal operators. Conditions implying commutativity of normal operators are given, without using the known 2πi-congruence-free hypothesis. This is a continuation of a recent work by the second author.
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.
V. Rakočević (1985)
Matematički Vesnik
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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 (Ω): (T 1 f)(x, y) = k 1(x, s, y)f(s, y)ds, (T 2 f)(x, y) = 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...
Djordjević, Slaviša V. (1997)
Matematichki Vesnik
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Andrzej Sołtysiak (1989)
Colloquium Mathematicae
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Slaviša V. Đorđević (1998)
Matematički Vesnik
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S. Djordjević, B. Duggal (2000)
Studia Mathematica
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We show that p-hyponormal operators obey Weyl's and a-Weyl's theorem. Also, we show that the spectrum, Weyl spectrum, Browder spectrum and approximate point spectrum are continuous functions in the class of all p-hyponormal operators.