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On norm closed $z$-invariant subspaces of $H^\infty$ (Harmonic, Analytic function spaces and Linear Operators, II)

On norm closed $z$-invariant subspaces of $H^\infty$ (Harmonic, Analytic function spaces and Linear Operators, II)
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Nontrivial invariant subspaces of linear operator pencils

Canadian Mathematical Bulletin, 2023
AbstractIn this paper, we introduce the spherical polar decomposition of the linear pencil of an ordered pair $\mathbf {T}=(T_{1},T_{2})$ and investigate nontrivial invariant subspaces between the generalized spherical Aluthge transform of the linear pencil of $\mathbf {T}$ and the linear pencil of the original pair $\mathbf {T}$ of bounded ...
Kim, Jaewoong, Yoon, Jasang
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Two invariant subspaces and spectral properties of a linear operator

Acta Scientiarum Mathematicarum, 2016
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Djordjević, S. V., Hwang, I. S., Duggal, B. P.   +2 more
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Error Bounds for Approximate Invariant Subspaces of Closed Linear Operators

SIAM Journal on Numerical Analysis, 1971
Let A be a closed linear operator on a separable Hilbert space $\mathcal{H}$ whose domain is dense in $\mathcal{H}$ Let $\mathcal{X}$ be a subspace of $\mathcal{H}$ contained in the domain of A and let $\mathcal{Y}$ be its orthogonal complement. Let B and C be the compressions of A to $\mathcal{Z}$ and $\mathcal{Y}$ respectively, let $G = Y^ * AX ...
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On the Variety of Invariant Subspaces of a Finite-Dimensional Linear Operator

Transactions of the American Mathematical Society, 1982
If V V is a finite-dimensional vector space over R \mathbf {R} or C \mathbf {C} and A ∈ Hom ( V ) A \in {\operatorname {Hom}}(V) , the set S A
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On Classification of Invariant Subspaces of a Linear Operator

1989
The problem of the classification of invariant subspaces of a linear operator is shown to be at least as complex as the problem of the classification of arbitrary pairs of square matrices up to simultaneous similarity.
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Lifting and linear maps of invariant subspaces among the linear pencil, a pair of operators, and their operator transforms

Communications in Nonlinear Science and Numerical Simulation
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Kim, Jaewoong, Yoon, Jasang
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Invariant Semi-definite Subspaces of Linear Operators in Krein Spaces

1974
The existence of invariant maximal uniformly definite (Section 1) resp. maximal semi-definite (Sections 2–3) subspaces is treated. In Sections 4–5 an application to quadratic pencils of Hilbert space operators is given. Section 6 contains the statement of some results concerning the spectral function of a positive or positizable selfadjoint operator in
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Structure of Closed Linear Translation Invariant Subspaces of A() and Kernels of Analytic Convolution Operators

1984
Publisher Summary This chapter presents notes on some progress concerning the study of such questions that has been made by the work of Berenstein and Taylor, Meise, and Schwerdtfeger . Even though the results are rather general, the chapter restricts the attention to the special situation introduced in the chapter because this allows a clear ...
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Note on the Invariant Subspaces of Linear Operators

Rendiconti del Circolo Matematico di Palermo, 1959
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