We also establish relations between cvp(H), {T∈cvp(G |suppT⊂H} and cvp(G) where cvp is the norm closure, in the set of all bounded operators of Lp, of the set all convolution operators with compact support.
A result of Rudin implies that bounded operators on the Banach space C [0,ω1]) of continuous functions on the ordinal interval [0,ω1] have a natural representation as [0,ω1]-matricesatrices.
But is a bounded operator on the set of continuous functions endowed with the uniform norm.
It is a bounded operator on the set of uniformly bounded functions endowed with the uniform topology.
It is a bounded operator on the space of continuous bounded functions endowed with the uniform norm.
The operator ℓ is an arbitrary linear and bounded operator on the space of left-continuous regulated on [ a, b ] vector valued functions and is represented by the Kurzweil-Stieltjes integral.
Operator ⁎-modules are generalizations of Hilbert C⁎-modules where the category of C⁎-algebras has been replaced by a more flexible category of involutive algebras of bounded operators: The operator ⁎-algebras.
We denote by a Banach space, the space of all linear and bounded operators on, and the space of all -valued continuous functions on.
We denote by a Banach space, the Banach space of all linear and bounded operators on, and the space of all -valued continuous functions on.
Theorem 2.1 The operator P 0 is an isomorphism between the spaces and L 2 ( R + ; H ). Proof First, we note that if ξ ∈ H 5 / 2, then e − t A ξ ∈ W 2 3 ( R + ; H ) and if η ∈ H 3 / 2, then t A e − t A η ∈ W 2 3 ( R + ; H ) (see, e.g., [23]), where e − t A is the strongly continuous semi-group of bounded operators generated by the operator −A.
