Riesz basis property of Hill operators with potentials in weighted spaces

Deviations of Riesz Projections of Hill Operators with Singular Potentials

Bari-markus Property for Riesz Projections of Hill Operators with Singular Potentials

A. Savchuk and A. Shkalikov [17] gave thorough spectral analysis of such operators. In particular, they consider a broad class of boundary conditions (bc) – see (1.6), Theorem 1.5 there – in terms of a function y and its quasi–derivative u = y′ −Qy. The natural form of periodic or antiperiodic (Per±) bc is the following one: (1.3) Per± : y(π) = ±y(0), u(π) = ±u(0) If the potential v happens to ...

Boundedness for Riesz transform associated with Schrödinger operators and its commutator on weighted Morrey spaces related to certain nonnegative potentials

*Correspondence: [email protected] School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, China Abstract Let L = – + V be a Schrödinger operator, where is the Laplacian on Rn and the nonnegative potential V belongs to the reverse Hölder class Bq for q≥ n/2. The Riesz transform associated with the operator L is denoted by T =∇(– + V)– 2 and the dual Ri...

ON RIESZ SPACES WITH b-PROPERTY AND b-WEAKLY COMPACT OPERATORS

An operator T : E → X between a Banach lattice E and a Banach space X is called b-weakly compact if T (B) is relatively weakly compact for each b-bounded set B in E. We characterize b-weakly compact operators among o-weakly compact operators. We show summing operators are b-weakly compact and discuss relation between Dunford–Pettis and b-weakly compact operators. We give necessary conditions fo...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...