On a Weyl-von Neumann -type Theorem for Antilinear Self-adjoint Operators

Ruotsalainen, Santtu

doi:10.48550/arxiv.1203.4670

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2014

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“…We next obtain a spectral theorem for bounded antilinear self-adjoint operators. For an approach using spectral integrals, see [20].…”

Section: [N]mentioning

confidence: 99%

Function theory and spectral mapping theorems for antilinear operators

Huhtanen¹,

Perämäki²

2014

J. Operator Theory

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Unlike in complex linear operator theory, polynomials or, more generally, Laurent series in antilinear operators cannot be modelled with complex analysis. There exists a corresponding function space, though, surfacing in spectral mapping theorems. These spectral mapping theorems are inclusive in general. Equality can be established in the self-adjoint case. The arising functions are shown to possess a biradial character. It is shown that to any given set of Jacobi parameters corresponds a biradial measure yielding these parameters in an iterative orthogonalization process in this function space, once equipped with the corresponding L 2 structure.

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“…We next obtain a spectral theorem for bounded antilinear self-adjoint operators. For an approach using spectral integrals, see [20].…”

Section: [N]mentioning

confidence: 99%