Operator valued roots of abelian analytic functions

Gilfeather, Frank

doi:10.2140/pjm.1974.55.127

Cited by 14 publications

(9 citation statements)

References 13 publications

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“…Each operator in a finite type I von Neumann algebra is a direct integral of operators acting on finite dimensional spaces, and is thus a direct sum of spectral operators by Azoff's result. In [14] it was proved that each root of an abelian analytic operator-valued function is unitarily equivalent to a countable direct sum of spectral operators (see [14] for terminology and details). We now show that each direct sum of spectral operators is quasisimilar to a spectral operator.…”

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confidence: 99%

A note on quasisimilarity. II

Fialkow¹

1977

Pacific J. Math.

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confidence: 99%

A note on quasisimilarity. II

Fialkow¹

1977

Pacific J. Math.

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“…We shall now consider bounded operators A in complex Hilbert spaces H. The operator norm of A ∈ B(H) is denoted by A . Polynomially normal operators have been discussed in [4], [7], as operator valued roots for polynomial equations p(z) − N = 0 with N normal. We formulate a structure result (see Theorem 3.1, in [7], also Theorem 2 in [8] ).…”

Section: Polynomially Normal Operators In Hilbert Spacesmentioning

confidence: 99%

Polynomial as a new variable - a Banach algebra with a functional calculus

Nevanlinna¹

2016

Operators and Matrices

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Abstract. Given any square matrix or a bounded operator A in a Hilbert space such that p(A) is normal (or similar to normal), we construct a Banach algebra, depending on the polynomial p , for which a simple functional calculus holds. When the polynomial is of degree d , then the algebra deals with continuous C d -valued functions, defined on the spectrum of p(A) . In particular, the calculus provides a natural approach to deal with nontrivial Jordan blocks and one does not need differentiability at such eigenvalues.Mathematics subject classification (2010): 15A60, 46J10, 47A60.

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“…operators have been extensively studied and many beautiful results have been obtained (see [5] and its references).…”

Section: Roots Of Normalmentioning

confidence: 99%