Triangular Operators

Herrero, Domingo A.

doi:10.1112/blms/23.6.513

Cited by 9 publications

(5 citation statements)

References 59 publications

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“…Because the transition matrix is upper triangular, the diagonal elements aa T are its eigenvalues [22]. Using (2.2):…”

Section: Uni-variable Recurrences Of Depth Onementioning

confidence: 99%

Carleman Linearization and Systems of Arbitrary Depth Polynomial Recursions

Mikołaj¹

2022

ALAMT

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New approach to systems of polynomial recursions is developed based on the Carleman linearization procedure. The article is divided into two main sections: firstly, we focus on the case of uni-variable depth-one polynomial recurrences. Subsequently, the systems of depth-one polynomial recurrence relations are discussed. The corresponding transition matrix is constructed and upper triangularized. Furthermore, the powers of the transition matrix are calculated using the back substitution procedure. The explicit expression for a solution to a broad family of recurrence relations is obtained. We investigate to which recurrences the framework can be applied and construct sufficient conditions for the method to work. It is shown how introduction of auxiliary variables can be used to reduce arbitrary depth systems to the depth-one system of recurrences dealt with earlier. Finally, the limitations of the method are discussed, outlining possible directions for future research.

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“…Because the transition matrix is upper triangular, the diagonal elements aa T are its eigenvalues [22]. Using (2.2):…”

Section: Uni-variable Recurrences Of Depth Onementioning

confidence: 99%

Carleman Linearization and Systems of Arbitrary Depth Polynomial Recursions

Mikołaj¹

2022

ALAMT

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“…That is, there exists an orthonormal basis (e n ) ∞ n=1 for H such that Te j , e i = 0 whenever i > j. We refer the reader to [14, Chapter 3], [7] and [15] for more information about the triangular operators. The operator T is called bitriangular if both T and T * are triangular, perhaps with respect to different orthonormal bases.…”

Section: Theorem Every Triangularizable Operator T With Countable Spe...mentioning

confidence: 99%

On almost-invariant subspaces and approximate commutation

Marcoux

Popov

Radjavi

2013

Journal of Functional Analysis

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A closed subspace of a Banach space X is almost-invariant for a collection S of bounded linear operators on X if for each T ∈ S there exists a finite-dimensional subspace F T of X such that TY ⊆ Y + F T . In this paper, we study the existence of almostinvariant subspaces of infinite dimension and codimension for various classes of Banach and Hilbert space operators. We also examine the structure of operators which admit a maximal commuting family of almost-invariant subspaces. In particular, we prove that if T is an operator on a separable Hilbert space and if TP − PT has finite rank for all projections P in a given maximal abelian self-adjoint algebra M then T = M + F where M ∈ M and F is of finite rank.

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“…It is in effect unitary diagonalizability, and as such more stringent than other, more general definitions of diagonalizability for Hilbert space operators, cf. [17].…”

Section: The Main Theoremmentioning

confidence: 99%

On a Weyl–von Neumann type theorem for antilinear self-adjoint operators

Ruotsalainen

2012

Studia Math.

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Abstract. Antilinear operators on a complex Hilbert space arise in various contexts in mathematical physics. In this paper, an analogue of the Weyl-von Neumann theorem for antilinear self-adjoint operators is proved, i.e. that an antilinear self-adjoint operator is the sum of a diagonalizable operator and of a compact operator with arbitrarily small Schatten p-norm. In doing so, we discuss conjugations and their properties. A spectral integral representation for antilinear self-adjoint operators is constructed.Mathematics Subject Classification (2010). Primary 47A10; Secondary 47B38.

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Triangular Operators

Cited by 9 publications

References 59 publications

Carleman Linearization and Systems of Arbitrary Depth Polynomial Recursions

Carleman Linearization and Systems of Arbitrary Depth Polynomial Recursions

On almost-invariant subspaces and approximate commutation

On a Weyl–von Neumann type theorem for antilinear self-adjoint operators

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