Closed linear operators with domain containing their range

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.

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.

Operators with numerical range in a closed halfplane

Various characterizations are given of real and complex Hilbert space operators with the numerical range in a closed halfplane.

Relatively Closed Operators and Linear Evolution Equations

In this paper it is shown how the vector-valued Laplace transform can be used to obtain existence and uniqueness results for exponentially bounded solutions of abstract linear evolution equations in Banach spaces. The method allows to consider problems for which the characteristic operator is, like many sums, products or limits of closed operators, not necessarily closed or closable.

Linear Operators and Their Spectra