Weakly invariant subspaces for multivalued linear operators on Banach spaces

Multivalued Linear Operators and Differential Inclusions in Banach Spaces

In this paper, we study multivalued linear operators (MLO’s) and their resolvents in non reflexive Banach spaces, introducing a new condition of a minimal growth at infinity, more general than the HilleYosida condition. Then we describe the generalized semigroups induced by MLO’s. We present a criterion for an MLO to be a generator The work of A. Baskakov and V. Obukhovskii is partially support...

ε-weakly Chebyshev subspaces and quotient spaces

Lomonosov’s Invariant Subspace Theorem for Multivalued Linear Operators

The famous Lomonosov’s invariant subspace theorem states that if a continuous linear operator T on an infinite-dimensional normed space E “commutes” with a compact operator K 6= 0, i.e., TK = KT, then T has a non-trivial closed invariant subspace. We generalize this theorem for multivalued linear operators. We also provide some applications to singlevalued linear operators.

Linear operators of Banach spaces with range in Lipschitz algebras

In this paper, a complete description concerning linear operators of Banach spaces with range in Lipschitz algebras $lip_al(X)$ is provided. Necessary and sufficient conditions are established to ensure boundedness and (weak) compactness of these operators. Finally, a lower bound for the essential norm of such operators is obtained.

Some properties of b-weakly compact operators on Banach lattices

In this paper we give some necessary and sufficient conditions for which each Banach lattice  is    space and we study some properties of b-weakly compact operators from a Banach lattice  into a Banach space . We show that every weakly compact operator from a Banach lattice  into a Banach space  is b-weakly compact and give a counterexample which shows that the inverse is not true but we prove ...