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Spring 2019 Partial isometries and a general spectral theorem
Bela Nagy
Adv. Oper. Theory 4(2): 351-368 (Spring 2019). DOI: 10.15352/aot.1804-1355

Abstract

‎We prove a general spectral theorem for an arbitrary densely defined closed linear operator $T$ between complex Hilbert‎ ‎spaces $H$ and $K$‎. ‎The corresponding operator measure is partial isometry valued and has properties similar to those of the resolution of‎ ‎the identity of a non-negative self-adjoint operator‎. ‎The main method is the use of the canonical factorization (polar decomposition) obtained‎ ‎by v‎. ‎Neumann and Murray‎. ‎The uniqueness of the generalized resolution of the identity is studied together with the properties of a (non-multiplicative)‎ ‎functional calculus‎. ‎The properties of this generalized resolution of the identity are also investigated‎.

Citation

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Bela Nagy. "Partial isometries and a general spectral theorem." Adv. Oper. Theory 4 (2) 351 - 368, Spring 2019. https://doi.org/10.15352/aot.1804-1355

Information

Received: 28 April 2018; Accepted: 27 August 2018; Published: Spring 2019
First available in Project Euclid: 20 September 2018

zbMATH: 07009313
MathSciNet: MR3895008
Digital Object Identifier: 10.15352/aot.1804-1355

Subjects:
Primary: 47B25
Secondary: 47A60 , 47B15

Keywords: ‎canonical factorization‎ , ‎‎closed densely defined linear operator , ‎general spectral theorem , Hilbert space , ‎partial isometry valued measure‎

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.4 • No. 2 • Spring 2019
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