For a separable complex Hilbert space H, we say that bounded linear operator T acting on H is C-normal, where C conjugation if it satisfies CT∗TC=TT∗. normal operator, give geometric conditions which guarantee its rank-one perturbation C-normal for some C. We also obtain new properties revealing the structure of operators.

The purpose of the paper was to investigate by kernel method a nonparametric estimate conditional density function scalar response variable given random taking values in separable real Hilbert space when observations are quasi-associated dependent. Under some general conditions, authors established pointwise almost complete consistencies with rates this estimator. principal aim is convergence r...

We show that the image of a commutative monotone sequentially complete C∗-algebra, under a sequentially normal morphism, is again a monotone sequentially complete C-algebra, and also a monotone sequentially closed C∗-subalgebra. As a consequence, the image of an algebra of this type, under a sequentially normal representation in a separable Hilbert space, is strongly closed. In the case of a un...

In applications, many states given for a system can be expressed by orthonormal elements, called “state elements”, taken in separable Hilbert space (called space”). The exact nature of the depends on system; example, state position and momentum is square-integrable functions. symmetries quantum represented class unitary operators that act space. ladder have effect lowering or raising energy sta...

‎We prove that a remainder $Y$ of a non-locally compact‎ ‎rectifiable space $X$ is locally a $p$-space if and only if‎ ‎either $X$ is a Lindel"{o}f $p$-space or $X$ is $sigma$-compact‎, ‎which improves two results by Arhangel'skii‎. ‎We also show that if a non-locally compact‎ ‎rectifiable space $X$ that is locally paracompact has a remainder $Y$ which has locally a $G_{delta}$-diagonal‎, ‎then...

Let A be a bounded operator on a separable, infinite dimensional Hilbert space H. Moreover, assume that A is not in the set C + K(H) of operators expressible as a sum of a scalar multiple of identity and a compact operator. What is the smallest similarity invariant semigroup containing operator A? Equivalently, which operators can be expressed as products of operators, similar to A? A partial a...

In the present paper, we prove spectral mapping theorem for (m,n)-paranormal operator T on a separable Hilbert space, that is, f (?w(T)) = ?w(f(T)) when is an analytic function some open neighborhood of ?(T). We also show T, Weyl?s holds, ?(T)-?w(T) ?00(T). Moreover, if algebraically (m,n)-paranormal, then and hold.

In the first part we have shown that, for L2-approximation of functions from a separable Hilbert space in worst-case setting, linear algorithms based on function values are almost as powerful arbitrary if widths square-summable. That is, they achieve same polynomial rate convergence. this sequel, prove similar result Banach spaces and other classes functions.

This work presents a parametrized family of distances, namely the Alpha Procrustes on set symmetric, positive definite (SPD) matrices. The distances provide unified formulation encompassing both Bures-Wasserstein and Log-Euclidean between SPD We show that are Riemannian corresponding to metrics manifold matrices, which encompass Wasserstein metrics. is then generalized Hilbert-Schmidt operators...