On spectra of Lüders operations | Zendy

Gabriel Nagy | Zendy

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On spectra of Lüders operations

Author(s) -

Gabriel Nagy

Publication year - 2008

Publication title -

journal of mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.708

H-Index - 119

eISSN - 1089-7658

pISSN - 0022-2488

DOI - 10.1063/1.2840472

Subject(s) - hilbert space , eigenvalues and eigenvectors , mathematics , spectrum (functional analysis) , pure mathematics , space (punctuation) , combinatorics , physics , computer science , quantum mechanics , operating system

We show that all the eigenvalues of certain generalized Luders operations are non-negative real numbers in two cases of interest. In particular, given a commuting n-tuple A=(A1,…,An) consisting of positive operators on a Hilbert space H, satisfying ∑j=1nAj=I, we show that the spectrum of the Luders operation: ΛA:B(H)∋X↦∑j=1nAj1∕2XAj1∕2∈B(H) is contained in [0,∞), so the only solution of the equation ΛA(X)=I−X is the “expected” one: X=12I.

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