Related papers: On Convergence of Conditional Expectation Operator…
A conjugate operator $T$ of one-dimensional harmonic oscillator $N$ is defined by an operator satisfying canonical commutation relation $[N,T]=-i\one$ on some domain but not necessarily a dense one. Examples of conjugate operators include…
We derive Miura operators for $W$- and $Y$-algebras from first principles as the expectation value of the intersection between a topological line defect and a holomorphic surface defect in 5-dimensional non-commutative $\mathfrak{gl}(1)$…
In the present paper deals with asymptotical stability of Markov operators acting on abstract state spaces (i.e. an ordered Banach space, where the norm has an additivity property on the cone of positive elements). Basically, we are…
We give necessary and sufficient conditions for a bounded operator defined between complex Hilbert spaces to be absolutely norm attaining. We discuss structure of such operators in the case of self-adjoint and normal operators separately.…
The relationship between the operator approximation property and the strong operator approximation property has deep significance in the theory of operator algebras. The original definitions of Effros and Ruan, unlike the classical…
In this paper, we introduce a large class of (so-called) conditional indicators, on a complete probability space with respect to a sub $\sigma$-algebra. A conditional indicator is a positive mapping, which is not necessary linear, but may…
We present new conditions for semigroups of positive operators to converge strongly as time tends to infinity. Our proofs are based on a novel approach combining the well-known splitting theorem by Jacobs, de Leeuw and Glicksberg with a…
We investigate the almost everywhere convergence of sequences of convolution operators given by probability measures $\mu_n$ on $\mathbb R$. If this sequence of operators constitutes an approximate identity on a particular class of…
In this article we prove martingale type pointwise convergence theorems pertaining to tensor product splines defined on $d$-dimensional Euclidean space ($d$ is a positive integer), where conditional expectations are replaced by their…
We consider sequences of operators $U_n:L^1(X)\to M(X)$, where $X$ is a space of homogeneous type. Under certain conditions on the operators $U_n$ we give a complete characterization of convergence (divergence) sets of functional sequences…
A necessary and sufficient condition on a sequence $\{\mathfrak{A}_n\}_{n\in \mathbb{N}}$ of $\sigma$-subalgebras that assures convergence almost every where of conditional expectations is given.
The aim of this paper is to give strict fixed point principles for multivalued operators $T:X\rightarrow P(X)$ satisfying some contraction conditions of \'Ciri\' c and of \'Ciri\' c-Reich-Rus type. We are interested, under which conditions,…
This work addresses the resolvent convergence of generalized MIT bag operators to Dirac operators with zigzag type boundary conditions. We prove that the convergence holds in strong but not in norm resolvent sense. Moreover, we show that…
In this paper we investigate boundedness, polar decomposition and spectral decomposition of weighted conditional expectation type operators on L^2(\Sigma).
We analyze various consequences in relation to the extension of operators $T:X\to Y$ that are $p$-compact, as well as the extension of operators $T:X\to Y$ whose adjoints $T^*:Y^*\to X^*$ are $p$-compact. In most cases, we discuss these…
When $L$ is the Hermite or the Ornstein-Uhlenbeck operator, we find minimal integrability and smoothness conditions on a function $f$ so that the fractional power $L^\sigma f(x_0)$ is well-defined at a given point $x_0$. We illustrate the…
In operator algebra theory, a conditional expectation is usually assumed to be a projection map onto a sub-algebra. In the paper, a further type of conditional expectation and an extension of the Lueders - von Neumann measurement to…
An NP-hard combinatorial optimization problem $\Pi$ is said to have an {\em approximation threshold} if there is some $t$ such that the optimal value of $\Pi$ can be approximated in polynomial time within a ratio of $t$, and it is NP-hard…
Given a complex, separable Hilbert space $\mathcal{H}$, we characterize those operators for which $\| P T (I-P) \| = \| (I-P) T P \|$ for all orthogonal projections $P$ on $\mathcal{H}$. When $\mathcal{H}$ is finite-dimensional, we also…
Convergence of operators acting on a given Hilbert space is an old and well studied topic in operator theory. The idea of introducing a related notion for operators acting on arying spaces is natural. However, it seems that the first…