Weighted projections into closed subspaces

In this paper we study $A$-projections, i.e. operators of a Hilbert space \HH which act as projections when a seminorm is considered in \HH. $A$-projections were introduced by Mitra and Rao \cite{[MitRao74]} for finite dimensional spaces. We relate this concept to the theory of compatibility between positive operators and closed subspaces of \HH. We also study the relationship between weighted least squares problems and compatibility

The representation and approximation for the weighted Minkowski inverse in Minkowski space

This paper extends some results for the weighted Moore–Penrose inverse in Hilbert space to the so-called weighted Minkowski inverse of an arbitrary rectangular matrix AMm,n in Minkowski spaces μ. Four methods are also used for approximating the weighted Minkowski Inverse . These methods are: Borel summable, Euler–Knopp summable, Newton–Raphson and Tikhonov’s methods

Regular covariant representations and their Wold-type decomposition

Olofsson introduced a growth condition regarding elements of an orbit for an expansive operator and generalized Richter's wandering subspace theorem. Later on, using the Moore-Penrose inverse, Ezzahraoui, Mbekhta, and Zerouali extended the growth condition and obtained a Shimorin-Wold-type decomposition. Shimorin-Wold-type decomposition for completely bounded covariant representations, which are close to isometric representations, is obtained in \cite{HV19}. This paper extends this decomposition for regular, completely bounded covariant representation having reduced minimum modulus $\geq 1$ that satisfies the growth condition. To prove the decomposition, we introduce the terms regular, algebraic core, and reduced minimum modulus in the completely bounded covariant representation setting and work out several fundamental results. Consequently, we shall analyze the weighted unilateral shift introduced by Muhly and Solel and introduce and explore a non-commutative weighted bilateral shift.Comment: 35 page

Characterization of coorbit spaces with phase-space covers

We show that coorbit spaces can be characterized in terms of arbitrary phase-space covers, which are families of phase-space multipliers associated with partitions of unity. This generalizes previously known results for time-frequency analysis to include time-scale decompositions. As a by-product, we extend the existing results for time-frequency analysis to an irregular setting.Comment: 31 pages. Revised version (title slightly changed). Typos fixe