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If T is a bounded operator on a separable complex Hilbert space ℋ, an invariant subspace ℳ for T is stable provided that whenever $T_{n}$ is a sequence of operators such that $‖ T_{n} - T ‖ \to 0$ , there is a sequence of subspaces $ℳ_{n}$ , with $ℳ_{n}$ in $L a t T_{n}$ for all n, such that $P_{ℳ_{n}} \to P_{ℳ}$ in the strong operator topology. If the projections converge in norm, ℳ is called a norm stable invariant subspace. This paper characterizes the stable invariant subspaces of the unilateral shift of finite multiplicity and normal operators. It also shows that...

Standard commuting dilations and liftings

Santanu Dey (2012)

Colloquium Mathematicae

We identify how the standard commuting dilation of the maximal commuting piece of any row contraction, especially on a finite-dimensional Hilbert space, is associated to the minimal isometric dilation of the row contraction. Using the concept of standard commuting dilation it is also shown that if liftings of row contractions are on finite-dimensional Hilbert spaces, then there are strong restrictions on properties of the liftings.

Strictly singular operators and the invariant subspace problem

C. Read (1999)

Studia Mathematica

Properties of strictly singular operators have recently become of topical interest because the work of Gowers and Maurey in [GM1] and [GM2] gives (among many other brilliant and surprising results, such as those in [G1] and [G2]) Banach spaces on which every continuous operator is of form λ I + S, where S is strictly singular. So if strictly singular operators had invariant subspaces, such spaces would have the property that all operators on them had invariant subspaces. However, in this paper we...

Structure of maximal spectral spaces of generalized scalar operators

Pavla Vrbová (1973)

Czechoslovak Mathematical Journal

Su un ampliamento della teorìa degli operatori lineari invarianti rispetto ad un gruppo di congruenze

Lucilla Bassotti Rizza (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let $A$ be an open subset of $\mathbb{R}^{n}$ , $W_{m}(A)$ the linear space of $m$ -vector valued functions defined on $A$ , $G\equiv\{\gamma\}$ a group of orthogonal matrices mapping $A$ onto itself and $T\equiv\{T_{\gamma}\}$ a linear representation of order $m$ of $G$ . A suitable group $\mathcal{T}(G,T)$ of linear operators of $W_{m}(A)$ is introduced which leads to a general definition of $T$ -invariant linear operator with respect to $G$ . When $G$ is a finite group, projection operators are explicitly obtained which define a "maximal" decomposition of the function space into a direct sum of subspaces...

Subespacios hiperinvariantes de operadores desplazamiento bilateral con sucesiones de pesos convergentes: {wn}, {w-n}, n = 1, ..., ∞.

Lucas Jódar (1985)

Stochastica

Estudiamos la existencia de subespacios hiperinvariantes de operadores desplazamiento bilateral ponderados e invertibles definidos sobre un espacio de Hilbert con base ortogonal {en}, n perteneciendo a Z, por la expresión T en = wn en+1, donde las sucesiones {wn} y {w-n}, con n = 1, ..., ∞, son convergentes.

Subspace Weyl-Heisenberg Frames.

J.-P. Gabardo, D. Han (2001)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

Sur le théorème de Alaoglu-Birkhoff

François Aribaud (1970/1971)

Séminaire Choquet. Initiation à l'analyse

Sur les opérateurs nilpotents d'ordre deux

Mohamed Barraa (1990)

Studia Mathematica

Sur les sous-espaces spectraux d'un opérateur compact relativement à une algèbre de von Neumann

Michel Hilsum (1978)

Annales de l'institut Fourier

Soit $T$ un opérateur compact dans une algèbre de Von Neumann. On montre que le sous-espace sup ker $(1 - T)^{n}$ est relativement fini.

The invariant subspace lattice of an algebraic operator.

Orovchanec, Marija, Nachevska, Biljana (2002)

Matematichki Vesnik

The Positive Supercyclicity Theorem.

F. León Saavedra (2004)

Extracta Mathematicae

We present some recent results related with supercyclic operators, also some of its consequences. We will finalize with new related questions.

The relationship between $K_{u}^{2} \cap v H^{2}$ and inner functions

Xiaoyuan Yang (2024)

Czechoslovak Mathematical Journal

Let $u$ be an inner function and $K_{u}^{2}$ be the corresponding model space. For an inner function $v$ , the subspace $v H^{2}$ is an invariant subspace of the unilateral shift operator on $H^{2}$ . In this article, using the structure of a Toeplitz kernel $\ker T_{\bar{u} v}$ , we study the intersection $K_{u}^{2} \cap v H^{2}$ by properties of inner functions $u$ and $v$ $(v ...$

Translation invariant subspaces of weighted l... and L... spaces.

Yngve Domar (1981)

Mathematica Scandinavica

Triangularization of some families of operators on locally convex spaces

Edvard Kramar (2001)

Commentationes Mathematicae Universitatis Carolinae

Some results concerning triangularization of some operators on locally convex spaces are established.

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