Quasireducible Operators

Carlos S. Kubrusly
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Carlos S. Kubrusly: Catholic University of Rio de Janeiro

Chapter 11 in Hilbert Space Operators, 2003, pp 117-128 from Springer

Abstract: Abstract An operator T on a complex Hilbert space is reducible if and only if there exists a nonscalar operator L such that LT = TL and T*L = LT* (Problem 8.16). That is, if and only if there exists a nonscalar L in {T}′ ⋂ {T*}′, where {T}′ denotes the commutant of T. Equivalently, T is reducible if and only if both T and T* lie in {L}′ for some nonscalar operator L. Quasireducibility was recently introduced in [34].

Keywords: Hilbert Space; Main Diagonal; Complex Hilbert Space; Diagonal Operator; Unital Algebra (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1007/978-1-4612-2064-0_11

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