Partial isometries and a general spectral theorem

  title={Partial isometries and a general spectral theorem},
  author={B{\'e}la Nagy},
  journal={Advances in Operator Theory},
  • B. Nagy
  • Published 1 April 2019
  • Mathematics
  • Advances in Operator Theory
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… 


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