On Multiplicative Lebesgue Integration and Families of Evolution Operators.
On sequences off linear functionals and some operators of the class .
On strongly stable approximations.
In this paper we prove that the convergence of (T - Tn)Tn-k to zero in operator norm (plus some technical conditions) is a sufficient condition for Tn to be a strongly stable approximation to T, thus extending some previous results existing in the literature.
On the approximation numbers of large Toeplitz matrices.
On the method of least squares of finding eigenvalues and eigenfunctions of some symmetric operators. II.
On λ-commuting operators
For a scalar λ, two operators T and S are said to λ-commute if TS = λST. In this note we explore the pervasiveness of the operators that λ-commute with a compact operator by characterizing the closure and the interior of the set of operators with this property.
Optimal order of convergence for stable evaluation of differential operators.
Positive operators and approximation in function spaces on completely regular spaces.
Preconditioners and Korovkin-type theorems for infinite-dimensional bounded linear operators via completely positive maps
The classical as well as noncommutative Korovkin-type theorems deal with the convergence of positive linear maps with respect to different modes of convergence, like norm or weak operator convergence etc. In this article, new versions of Korovkin-type theorems are proved using the notions of convergence induced by strong, weak and uniform eigenvalue clustering of matrix sequences with growing order. Such modes of convergence were originally considered for the special case of Toeplitz matrices and...
Sard's approximation processes and oblique projections
Three problems arising in approximation theory are studied. These problems have already been studied by Arthur Sard. The main goal of this paper is to use geometrical compatibility theory to extend Sard's results and get characterizations of the sets of solutions.
Spectral approximation of multiplication operators.
Sur les isométries partielles maximales essentielles
We study the problem of approximation by the sets S + K(H), , V + K(H) and where H is a separable complex Hilbert space, K(H) is the ideal of compact operators, is the set of isometries, V = S ∪ S* is the set of maximal partial isometries, and where π : B(H) → B(H)/K(H) denotes the canonical projection. We also prove that all the relevant distances are attained. This implies that all these classes are closed and we remark that . We also show that S + K(H) is both closed and open in ....
The strong unicity constant and its applications
In this report we discuss the applications of the strong unicity constant and highlight its use in the minimal projection problem.
The strong unicity constant for projections.
Über die Approximation von linearen Glechungen zweiter Art und Eigenwertproblemen in Banach-Räumen.
Über die Konvergenzgeschwindigkeit projektiver Verfahren. II.
Universal stability of Banach spaces for ε -isometries
Let X, Y be real Banach spaces and ε > 0. A standard ε-isometry f: X → Y is said to be (α,γ)-stable (with respect to for some α,γ > 0) if T is a linear operator with ||T|| ≤ α such that Tf- Id is uniformly bounded by γε on X. The pair (X,Y) is said to be stable if every standard ε-isometry f: X → Y is (α,γ)-stable for some α,γ > 0. The space X[Y] is said to be universally left [right]-stable if (X,Y) is always stable for every Y[X]. In this paper, we show that universally right-stable...
Weighted projections into closed subspaces
We study A-projections, i.e. operators on a Hilbert space 𝓗 which act as projections when a seminorm is considered in 𝓗. The A-projections were introduced by Mitra and Rao (1974) for finite-dimensional spaces. We relate this concept to the theory of compatibility between positive operators and closed subspaces of 𝓗. We also study the relationship between weighted least squares problems and compatibility.
О критериях сходимости аппроксимаций метода регуляризации.
О некорректно поставленных задачах