The spectral function for some products of self-adjoint operators. (English. Russian original) Zbl 1146.47012
Math. Notes 81, No. 6, 847-850 (2007); translation from Mat. Zametki 81, No. 6, 948-951 (2007).
Let \(A\) and \(G\) be two (non-commuting) bounded self-adjoint Hilbert space operators. In this note, the author constructs a spectral measure for their product \(AG\) under some reasonable additional restrictions on them.
Reviewer: Khristo N. Boyadzhiev (Ada)
MSC:
| 47B25 | Linear symmetric and selfadjoint operators (unbounded) |
Keywords:
selfadjoint linear operator; \(G\)-selfadjoint operator; \(G\)-spectral function; homomorphism; Hilbert space; sesquilinear form; strong operator topologyReferences:
| [1] | H. Langer, Math. Nachr. 33(1–2), 107 (1967). · Zbl 0147.12102 · doi:10.1002/mana.19670330109 |
| [2] | T. Ya. Azizov and I. S. Iokhvidov, Foundations of Theory of Linear Operators in Spaces with Indefinite Metric (Nauka, Moscow, 1986) [in Russian]. |
| [3] | J. Bognár, Acta Sci. Math. (Szeged) 45(1–4), 75 (1983). |
| [4] | A. I. Plesner, Spectral Theory of Linear Operators (Nauka, Moscow, 1965) [in Russian]. · Zbl 0147.34301 |
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