On operators with the same spectrum
Gh. Constantin (1975)
Matematički Vesnik
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Gh. Constantin (1975)
Matematički Vesnik
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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.
Jaroslav Zemánek (2007)
Banach Center Publications
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Andrzej Sołtysiak (1989)
Colloquium Mathematicae
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Djordjević, Slaviša V. (1997)
Matematichki Vesnik
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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).
Catană, Petronela (2005)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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H. J. Borchers (1986)
Recherche Coopérative sur Programme n°25
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GH. Mocanu (1974)
Studia Mathematica
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Edward B. Burger, Amanda Folsom, Alexander Pekker, Rungporn Roengpitya, Julia Snyder (2002)
Acta Arithmetica
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V. Rakočević (1985)
Matematički Vesnik
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Andrzej Pokrzywa (1985)
Studia Mathematica
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V. Rakočević (1981)
Matematički Vesnik
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W. Żelazko, Z. Słodkowski (1974)
Studia Mathematica
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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.