Radial limits in co-invariant subspaces
Reducible representations of abelian groups
A criterion for reducibility of certain representations of abelian groups is established. Among the applications of this criterion, we give a positive answer to the translation invariant subspace problem for weighted spaces on locally compact abelian groups, for even weights and .
Reductive Algebras with Minimal Ideals.
Reflexive families of closed sets
Let S(X) denote the set of all closed subsets of a topological space X, and C(X) the set of all continuous mappings f:X → X. A family 𝓐 ⊆ S(X) is called reflexive if there exists ℱ ⊆ C(X) such that 𝓐 = {A ∈ S(X): f(A) ⊆ A for every f ∈ ℱ}. We investigate conditions ensuring that a family of closed subsets is reflexive.
Reflexive Operator Algebras on Non-Commutative Hardy Spaces.
Reflexivity of bilattices
We study reflexivity of bilattices. Some examples of reflexive and non-reflexive bilattices are given. With a given subspace lattice we may associate a bilattice . Similarly, having a bilattice we may construct a subspace lattice . Connections between reflexivity of subspace lattices and associated bilattices are investigated. It is also shown that the direct sum of any two bilattices is never reflexive.
Reflexivity of isometries
We prove that any set of commuting isometries on a separable Hilbert space is reflexive.
Regularity problem for extremal vectors.
In this paper, we will use results developed by Ansari and Enflo in the theory of bounded linear operators with dense range. We define two maps, with regards to some parameters, that control surjectivity default of a given operator, and prove analycity for the first one and global continuity for the other one. Minimisation results are also obtained in relation to this study.
Remarks on separation of convex sets, fixed-point theorem, and applications in theory of linear operators.
Renormalized solutions for nonlinear degenerate elliptic problems with L1 data.
Representations of groups on eigenspaces of invariant differential operators
Representations of H...(G) and invariant subspaces.
Representations of semigroups and extension of invariant linear functionals.
Resolvent Vectors, Invariant Subspaces, and Sets of Zero Capacity.
Rings of PDE-preserving operators on nuclearly entire functions
Let E,F be Banach spaces where F = E’ or vice versa. If F has the approximation property, then the space of nuclearly entire functions of bounded type, , and the space of exponential type functions, Exp(F), form a dual pair. The set of convolution operators on (i.e. the continuous operators that commute with all translations) is formed by the transposes , φ ∈ Exp(F), of the multiplication operators φ :ψ ↦ φ ψ on Exp(F). A continuous operator T on is PDE-preserving for a set ℙ ⊆ Exp(F) if it...
Selfadjoint operator matrices with finite rows
A generalization of the Carleman criterion for selfadjointness of Jacobi matrices to the case of symmetric matrices with finite rows is established. In particular, a new proof of the Carleman criterion is found. An extension of Jørgensen's criterion for selfadjointness of symmetric operators with "almost invariant" subspaces is obtained. Some applications to hyponormal weighted shifts are given.
Similarity and compact perturbations of nest algebras.
Sobre los operadores desplazamiento ponderados sub-acotados.
We study the relation between the sets of cyclic vectors of an unilateral bounded below weighted shift operator T and T|S where S is an invariant subspace of T. It is proved that T can not be unicellular and known results are generalized.
Some invariant subspaces for A-contractions and applications
Some invariant subspaces for the operators A and T acting on a Hilbert space H and satisfying T*AT ≤ A and A ≥ 0, are presented. Especially, the largest invariant subspace for A and T on which the equality T* AT = A occurs, is studied in connections to others invariant or reducing subspaces for A, or T. Such subspaces are related to the asymptotic form of the subspace quoted above, this form being obtained using the operator limit of the sequence {T*nATn; n ≥ 1}. More complete results are given...
Some remarks on the invariant subspace problem for hyponormal operators.