Vol. 76, No. 1, 1978

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On the expansion in joint generalized eigenvectors

Klaus Kalb

Vol. 76 (1978), No. 1, 109–116

Let 𝒜 be a family commuting selfadjoint of (normal) operators in a complex (not necessarily separable) Hilbert space H. A natural triplet ϕ H ϕis described, such that (1) 𝒜 possesses a complete system of joint generalized eigenvectors in ϕ; (2) the joint generalized point spectrum of 𝒜 essentially coincides with the joint spectrum of 𝒜; (3) the generalized point spectra, generalized spectra and spectra essentially coincide for all A ∈𝒜; (4) the simultaneous diagonalization of 𝒜 in H by means of its spectral measure extends to ϕ. Also the multiplicity of the joint generalized eigenvectors of 𝒜 is discussed.

Mathematical Subject Classification 2000
Primary: 47A70
Secondary: 47B15
Received: 21 April 1977
Published: 1 May 1978
Klaus Kalb