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Strictly singular operators and the invariant subspace problem

C. Read (1999)

Studia Mathematica

Properties of strictly singular operators have recently become of topical interest because the work of Gowers and Maurey in [GM1] and [GM2] gives (among many other brilliant and surprising results, such as those in [G1] and [G2]) Banach spaces on which every continuous operator is of form λ I + S, where S is strictly singular. So if strictly singular operators had invariant subspaces, such spaces would have the property that all operators on them had invariant subspaces. However, in this paper we...

Subespacios hiperinvariantes de operadores desplazamiento bilateral con sucesiones de pesos convergentes: {wn}, {w-n}, n = 1, ..., ∞.

Lucas Jódar (1985)

Stochastica

Estudiamos la existencia de subespacios hiperinvariantes de operadores desplazamiento bilateral ponderados e invertibles definidos sobre un espacio de Hilbert con base ortogonal {en}, n perteneciendo a Z, por la expresión T en = wn en+1, donde las sucesiones {wn} y {w-n}, con n = 1, ..., ∞, son convergentes.

Superposition operator on the space of sequences almost converging to zero

Egor Alekhno (2012)

Open Mathematics

We study the superposition operator f on on the space ac 0 of sequences almost converging to zero. Conditions are derived for which f has a representation of the form f x = a+bx +g x, for all x ∈ ac 0 with a = f 0, b ∈ D(ac 0), g a superposition operator from ℓ∞ into I(ac 0), D(ac 0) = {z: zx ∈ ac 0 for all x ∈ ac 0}, and I(ac 0) the maximal ideal in ac 0. If f is generated by a function f of a real variable, then f is linear. We consider the conditions for which a bounded function f generates f...

Superposition operators on $W_{0} (ϕ)$ .

Supama, Darmawijaya, Soeparna (2004)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

Sur le spectre d'un shift à poids opérateurs.

M. Houimdi, M. Ouali (1998)

Extracta Mathematicae