On the Model and Invariant Subspaces for Pairs of Commuting Isometries
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DOI: 10.1007/s00020-019-2516-4
Abstract: The paper is devoted to a model and joint invariant subspaces under a pair of commuting isometries. A certain class of pairs of commuting isometries is defined. We give a model for such pairs and… read more here.
Keywords: commuting isometries; joint invariant; pair; model ... See more keywords
Representing Kernels of Perturbations of Toeplitz Operators by Backward Shift-Invariant Subspaces
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DOI: 10.1007/s00020-020-02592-7
Abstract: It is well known that the kernel of a Toeplitz operator is nearly invariant under the backward shift $S^*$. This paper shows that kernels of finite-rank perturbations of Toeplitz operators are nearly $S^*$-invariant with finite… read more here.
Keywords: toeplitz operators; backward shift; perturbations toeplitz; representing kernels ... See more keywords
Invariant subspaces and operator model theory on noncommutative varieties
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DOI: 10.1007/s00208-018-1714-8
Abstract: Let $${{\mathcal {Q}}}\subset {{\mathbb {C}}}\left$$Q⊂CZ1,…,Zn be an arbitrary set of polynomials in noncommutative indeterminates such that $$q(0)=0$$q(0)=0 for all $$q\in {{\mathcal {Q}}}$$q∈Q. The noncommutative variety $$\begin{aligned} {{\mathcal {V}}}_{f,{{\mathcal {Q}}}}^m({{\mathcal {H}}}):=\left\{ { X}=(X_1,\ldots , X_n)\in \mathbf{D}_f^m({{\mathcal… read more here.
Keywords: mathcal mathcal; space; model; operator model ... See more keywords
On Invariant Subspaces of the Pommiez Operator in the Spaces of Entire Functions of Exponential Type
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DOI: 10.1007/s10958-019-04461-0
Abstract: We describe closed invariant eigenspaces of the Pommmiez operator in the (LF)-space of entire functions of exponential type. This space is topologically equivalent (by means of the Laplace transform) to the strong dual space of… read more here.
Keywords: functions exponential; exponential type; operator; entire functions ... See more keywords
Convex analysis and non-trivial invariant subspaces
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DOI: 10.1007/s11117-019-00682-4
Abstract: We establish sufficient conditions for the existence of invariant subspaces for operators on real Banach spaces, and we investigate the behaviour of operators without such subspaces. All proofs are elementary. read more here.
Keywords: trivial invariant; convex analysis; non trivial; analysis non ... See more keywords
Approximation of Invariant Subspaces in Some Dirichlet-Type Spaces
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DOI: 10.1007/s11785-017-0706-0
Abstract: The Hilbert space $$\mathcal {D}_{2}$$D2 is the space of all holomorphic functions f defined on the open unit disc $$\mathbb {D}$$D such that $${f}^{'}$$f′ is in the Hardy Hilbert space $$\mathbf {H}^2.$$H2. In this paper,… read more here.
Keywords: subspaces dirichlet; space; type spaces; approximation invariant ... See more keywords
The commutant and invariant subspaces for dual truncated Toeplitz operators
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DOI: 10.1007/s43037-020-00102-w
Abstract: Dual truncated Toeplitz operators on the orthogonal complement of the model space $$K_u^2(=H^2 \ominus uH^2)$$ with u nonconstant inner function are defined to be the compression of multiplication operators to the orthogonal complement of $$K_u^2$$… read more here.
Keywords: dual truncated; commutant invariant; toeplitz operators; truncated toeplitz ... See more keywords
Nonuniform sampling in principal shift-invariant subspaces of mixed Lebesgue spaces Lp,q(Rd+1)
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DOI: 10.1016/j.jmaa.2017.04.036
Abstract: Abstract In this paper, we study the nonuniform sampling and reconstruction problem in shift-invariant subspaces of mixed Lebesgue spaces. We first show that shift-invariant subspaces in mixed Lebesgue spaces L p , q ( R… read more here.
Keywords: subspaces mixed; mixed lebesgue; lebesgue spaces; shift invariant ... See more keywords
The existence of Hall polynomials for x2-bounded invariant subspaces of nilpotent linear operators
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DOI: 10.1016/j.jpaa.2021.106921
Abstract: We prove the existence of Hall polynomials for x2-bounded invariant subspaces of nilpotent linear operators. read more here.
Keywords: bounded invariant; existence hall; hall polynomials; subspaces nilpotent ... See more keywords
The closedness of shift invariant subspaces in Lp,q(Rd+1)$L^{p,q} (\mathbb{R}^{d+1} )$
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DOI: 10.1186/s13660-018-1755-2
Abstract: In this paper, we consider the closedness of shift invariant subspaces in Lp,q(Rd+1)$L^{p,q} (\mathbb{R}^{d+1} )$. We first define the shift invariant subspaces generated by the shifts of finite functions in Lp,q(Rd+1)$L^{p,q} (\mathbb{R}^{d+1} )$. Then we… read more here.
Keywords: closedness shift; subspaces mathbb; shift invariant; invariant subspaces ... See more keywords
Constrained characteristic functions, multivariable interpolation, and invariant subspaces
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DOI: 10.1186/s13660-020-02412-x
Abstract: In this paper, we present a functional model theorem for completely non-coisometric n -tuples of operators in the noncommutative variety V f , φ , I ( H ) $\mathcal{V}_{f,\varphi,\mathcal{I}}(\mathcal{H})$ in terms of constrained characteristic… read more here.
Keywords: characteristic functions; functions multivariable; multivariable interpolation; constrained characteristic ... See more keywords