On a -polar decomposition of a bounded operator and matrices of -symmetric and -skew-symmetric operators.
On an integral operator in the space of functions with bounded variation
On an integral representation of antisymmetric operations in Hilbert spaces. I. Bounded operations
On isometries in linear metric spaces
On --normal and --quasinormal semi-Hilbertian space operators
The purpose of the paper is to introduce and study a new class of operators on semi-Hilbertian spaces, i.e. spaces generated by positive semi-definite sesquilinear forms. Let be a Hilbert space and let be a positive bounded operator on . The semi-inner product , , induces a semi-norm . This makes into a semi-Hilbertian space. An operator is said to be --normal if for some positive integers and .
On quasi-compactness of operator nets on Banach spaces
The paper introduces a notion of quasi-compact operator net on a Banach space. It is proved that quasi-compactness of a uniform Lotz-Räbiger net is equivalent to quasi-compactness of some operator . We prove that strong convergence of a quasi-compact uniform Lotz-Räbiger net implies uniform convergence to a finite-rank projection. Precompactness of operator nets is also investigated.
On Some Classes Of Linear Equations
On some classes of linear equations.
On some classes of linear equations, II.
On some new embedding theorems for some analytic classes in the unit ball.
On some properties of holomorphic spaces based on Bergman metric ball and Luzin area operator.
On spectral properties of linear combinations of idempotents
Let P,Q be two linear idempotents on a Banach space. We show that the closedness of the range and complementarity of the kernel (range) of linear combinations of P and Q are independent of the choice of coefficients. This generalizes known results and shows that many spectral properties of linear combinations do not depend on their coefficients.
On the local spectral radius in partially ordered Banach spaces
On the structure of commuting isometries
On Well-Located Subspaces of Distribution-Spaces.
Opérateurs uniformément convexifiants
Pelczynski’s property for Banach spaces
Perturbation of Maps in Locally Convex Spaces.
Powers of m-isometries
A bounded linear operator T on a Banach space X is called an (m,p)-isometry for a positive integer m and a real number p ≥ 1 if, for any vector x ∈ X, . We prove that any power of an (m,p)-isometry is also an (m,p)-isometry. In general the converse is not true. However, we prove that if and are (m,p)-isometries for a positive integer r, then T is an (m,p)-isometry. More precisely, if is an (m,p)-isometry and is an (l,p)-isometry, then is an (h,p)-isometry, where t = gcd(r,s) and h = min(m,l)....
Problèmes mathématiques de la théorie quantique des champs II : prolongement analytique