Factorization results related to shifts in an indefinite metric

DOI10.1007/BF01694058zbMath0499.47013MaRDI QIDQ1171740

Joseph A. Ball, J. William Helton

Publication date: 1982

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

zbMATH Keywords

indefinite inner productToeplitz operatorBeurling-Lax type representation for a simply invariant subspace for a shift operatorbounded measurable selfadjoint valued matrix functions on the unit circleDarlington embedding theoremindefinite metric analogues of inner-outer factorizationouter square-integrable matrix functionwinding matrix function

Mathematics Subject Classification ID

Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators (47A68) Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) (47B37) Spaces with indefinite inner product (Kre?n spaces, Pontryagin spaces, etc.) (46C20) Linear operators on spaces with an indefinite metric (47B50)

Related Items

Shift invariant subspaces, factorization, and interpolation for matrices. I. The canonical case, Normal projections in Krein spaces, Optimal normal projections in Krein spaces, Factorization of Hermitian matrix-valued functions and classification of shifts in a space with indefinite metric, Beurling-Lax representations using classical Lie groups with many applications. IV. GL(n,R), \(U^ *(2n)\), SL(n,\({\mathbb{C}})\), and a solvable group, Beurling-Lax representations using classical Lie groups with many applications. II: \(\mathrm{GL}(n,\mathbb C)\) and Wiener-Hopf factorization, Indefinite least-squares problems and pseudo-regularity, Non-Euclidean functional analysis and electronics, Interpolation problems of Pick-Nevanlinna and Loewner types for meromorphic matrix functions: Parametrization of the set of all solutions

Cites Work

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• Vectorial Toeplitz operators and the Fejer-Riesz theorem
• On two problems concerning linear transformations in Hilbert space
• The multiplicative structure of 𝐽-contractive matrix functions
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• Factorization of selfadjoint matrix polynomials with constant signature
• The factorization problem for nonnegative operator valued functions
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