We establish the characterisations of classes bounded linear operators from generalised Hahn sequence space hd, where d is an unbounded monotone increasing positive real numbers, into spaces w0, w and w? sequences that are strongly summable to zero, by Ces?ro method order one. Furthermore, we prove estimates for Hausdorff measure noncompactness hd w, identities use these results characterise co...

This paper aims to study fuzzy order bounded linear operators between two Riesz spaces. Two lattice operations are defined make the set of all as a space when codomain is Dedekind complete. As special case, separation property in dual studied. Furthermore, we studied norms compatible with ordering (fuzzy norm space) and discussed relation topological locally convex solid space.

It is shown that almost superdiagonal, polynomially compact operators on the sequence space l(p i) have nontrivial, closed invariant subspaces if the nonlocally convex linear topology τ(p i) is locally bounded. 1. Introduction. The purpose of this paper is to show that almost super-diagonal, polynomially compact operators on the sequence space l(p i) have nontrivial, closed invariant subspaces ...

1.1 (Fredholm operators). Let X, Y be real Banach spaces and denote their dual spaces by X, Y . A bounded linear operator D : X → Y is called Fredholm if it has a closed image and if its kernel and cokernel (the quotient space Y/imD) are finite dimensional. Equivalently, there exists a bounded linear operator T : Y → X such that the operators TD− idX and DT − idY are compact. The Fredholm index...

In this paper, we study frames for bounded linear operators and defined the notion of Ad-operator frame for Banach spaces. A necessary and sufficient condition for a sequence of bounded linear operators to be an Ad-operator frame has been given. Some characterizations of Ad-operator frames have been discussed. Further, a method has been given to generate a -Banach frame using a Schauder frame. ...

Under the generic assumption that zero is in the resolvent set of the generator, we show that the optimal control problem for a stable well-posed linear system is equivalent to a control problem for its reciprocal system which has bounded generating operators. Consequently, the operator X that defines the optimal cost satisfies a Riccati equation with bounded operators. Previous results needed ...

In the paper, we investigate weighted composition operators on Bergman spaces of a half-plane. We characterize which are hermitian and those complex symmetric with respect to family conjugations. As it turns out, enhanced by symmetry must be bounded. Hermitian, unitary proven an adapted highly relevant conjugation. classify linear fractional functions give rise bounded operators. end paper natu...

In this paper, we characterize generalized and hypergeneralized projections (bounded linear operators which satisfy conditions A = A∗ and A = A†). We give their matrix representations and examine under what conditions the product, difference and sum of these operators are operators of the same class.

It is shown that, for the spectral operators of scalar type, the well-known characterizations of the generation of C0and analytic semigroups of bounded linear operators can be reformulated exclusively in terms of the spectrum of such operators, the conditions on the resolvent of the generator being automatically met and the corresponding semigroup being that of the exponentials of the operator.