Champs hilbertiens faiblement continus et champs ultrafaiblement continus d’algèbres duales. (w * -continuous fields of Hilbert spaces and dual algebras)
Comptes Rendus de l Académie des Sciences - Series I - Mathematics
This article deals with some cyclic families of functions for antianalytic Toeplitz operators who... more This article deals with some cyclic families of functions for antianalytic Toeplitz operators whose symbol is a finite Blaschke product in the spaces H p where 1 < p < ∞. We give a description of the invariant subspaces for this type of operators generated by special decompositions and by lacunary decompositions of functions. To that end, we study some particular decomposition properties of a function in H p associated with an inner function which are valid in general.
Our purpose is to investigate various stability properties of the Aluthge transform of an operato... more Our purpose is to investigate various stability properties of the Aluthge transform of an operator acting on a Hilbert space H. We begin with the stability of partial isometries, with some examples in Hardy spaces. Then we obtain some interesting relations about minimum polynomial, iterated kernels and iterated ranges between an operator and its Aluthge transform. And we finish with an analysis of stability of C 0,· and C 1,· operator classes.
DESCRIPTION We say that a complex number λ is an extended eigenvalue of a bounded linear operator... more DESCRIPTION We say that a complex number λ is an extended eigenvalue of a bounded linear operator T on a Hilbert space H if there exists a nonzero bounded linear operator X acting on H, called extended eigen- vector associated to λ, and satisfying the equation T X = λXT . In this paper we describe the sets of extended eigenvalues and extended eigenvectors for the quasi-normal operators.
We are firstly interested in finding the best possible compressions for a polynomially bounded op... more We are firstly interested in finding the best possible compressions for a polynomially bounded operator T that belongs to the class A 1,1 intro-duced by H. Bercovici, C. Foia and C. Pearcy in [3]. Then, we use these compressions in order to obtain spatial factorizations, with a single vector, for large classes of lower semicontinuous positive functions f , in the sense that there exists a vector x in the Hilbert space H such that f (n) = T −n x|x, for all negative integer numbers n.
Let T be an absolutely continuous contraction acting on a Hilbert space. Its boundary set XT can ... more Let T be an absolutely continuous contraction acting on a Hilbert space. Its boundary set XT can be seen as a localization, on a Borel subset of the unit circle T, of a sequence condition whose validity on all of T is equiv- alent to membership of T in the classA@0. The main result is the following: if b is a Blaschke product of degree d for which there exist d distinct Mobius transforms u such that b - u = b, then b(XT) = Xb(T).
We give in this paper some asymptotic Von Neumann inequalities for power bounded operators in the... more We give in this paper some asymptotic Von Neumann inequalities for power bounded operators in the class C p Π C\ t and some spacial von Neumann inequalities associated with non zero elements of the point spectrum, when it is non void, of generalized Toeplitz operators.
We devote this note to the study of strict ρ-contractions. We characterize such operators in term... more We devote this note to the study of strict ρ-contractions. We characterize such operators in term on their restriction and quotient on some invariant subspace. Several special cases are discussed and some results in the scalar case are retrieved.
Champs hilbertiens faiblement continus et champs ultrafaiblement continus d’algèbres duales. (w * -continuous fields of Hilbert spaces and dual algebras)
Comptes Rendus de l Académie des Sciences - Series I - Mathematics
This article deals with some cyclic families of functions for antianalytic Toeplitz operators who... more This article deals with some cyclic families of functions for antianalytic Toeplitz operators whose symbol is a finite Blaschke product in the spaces H p where 1 < p < ∞. We give a description of the invariant subspaces for this type of operators generated by special decompositions and by lacunary decompositions of functions. To that end, we study some particular decomposition properties of a function in H p associated with an inner function which are valid in general.
Our purpose is to investigate various stability properties of the Aluthge transform of an operato... more Our purpose is to investigate various stability properties of the Aluthge transform of an operator acting on a Hilbert space H. We begin with the stability of partial isometries, with some examples in Hardy spaces. Then we obtain some interesting relations about minimum polynomial, iterated kernels and iterated ranges between an operator and its Aluthge transform. And we finish with an analysis of stability of C 0,· and C 1,· operator classes.
DESCRIPTION We say that a complex number λ is an extended eigenvalue of a bounded linear operator... more DESCRIPTION We say that a complex number λ is an extended eigenvalue of a bounded linear operator T on a Hilbert space H if there exists a nonzero bounded linear operator X acting on H, called extended eigen- vector associated to λ, and satisfying the equation T X = λXT . In this paper we describe the sets of extended eigenvalues and extended eigenvectors for the quasi-normal operators.
We are firstly interested in finding the best possible compressions for a polynomially bounded op... more We are firstly interested in finding the best possible compressions for a polynomially bounded operator T that belongs to the class A 1,1 intro-duced by H. Bercovici, C. Foia and C. Pearcy in [3]. Then, we use these compressions in order to obtain spatial factorizations, with a single vector, for large classes of lower semicontinuous positive functions f , in the sense that there exists a vector x in the Hilbert space H such that f (n) = T −n x|x, for all negative integer numbers n.
Let T be an absolutely continuous contraction acting on a Hilbert space. Its boundary set XT can ... more Let T be an absolutely continuous contraction acting on a Hilbert space. Its boundary set XT can be seen as a localization, on a Borel subset of the unit circle T, of a sequence condition whose validity on all of T is equiv- alent to membership of T in the classA@0. The main result is the following: if b is a Blaschke product of degree d for which there exist d distinct Mobius transforms u such that b - u = b, then b(XT) = Xb(T).
We give in this paper some asymptotic Von Neumann inequalities for power bounded operators in the... more We give in this paper some asymptotic Von Neumann inequalities for power bounded operators in the class C p Π C\ t and some spacial von Neumann inequalities associated with non zero elements of the point spectrum, when it is non void, of generalized Toeplitz operators.
We devote this note to the study of strict ρ-contractions. We characterize such operators in term... more We devote this note to the study of strict ρ-contractions. We characterize such operators in term on their restriction and quotient on some invariant subspace. Several special cases are discussed and some results in the scalar case are retrieved.
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Papers by Gilles Cassier