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- W2366051315 abstract "A bounded linear opertor T acting on a Hilbert space H is said to be Jsubnormal with order n if on some ∏_n-Pontrjagin space ∏ containing H, there exists a bounded J-normal operator (?) such that (?) f=Tf for every f in H and that ∏ is spanned by the elements of the from (?)f, where f∈H and k=0, 1, 2, ….Let H be a Hilbert space and let T be in B(H). The main purpose of this paper is to prove that the following statements are equivalent:(1) Tis J-subnormal with order n;(2) For each non-negative integer r and for each set {x_(ik): i, k=0, 1, …, r} of elements of H, the Hermitian from sum from i,j,k,l=0 to r (T~jx_(ik), T~ix_(jl)a_(ik)(?)_(jl)) has at most n negative squares, and for at least one choice of r and {x_(ik)}, it has exactly n negative squares;(3) The operator function e~(?)e~(ζT) is quasi-positive befinite with order n in the complex plane. This result is an extension of the theorems of Halmos and Brain." @default.
- W2366051315 created "2016-06-24" @default.
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- W2366051315 date "1982-01-01" @default.
- W2366051315 modified "2023-09-23" @default.
- W2366051315 title "ON THE J-NORMAL EXTENSIONS OF OPERATORS" @default.
- W2366051315 hasPublicationYear "1982" @default.
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