Given a Hilbert space and the generator A of a strongly continuous, exponentially stable, semigroup on this Hilbert space. For any g(−s) ∈ H∞ we show that there exists an inf nite-time admissible output operator g(A). If g is rational, then this operator is bounded, and equals the “normal” def nition of g(A). In particular, when g(s) = 1/(s + α), α ∈ C + 0 , then this admissible output operator...

We prove that if X and Y are operator spaces such that every completely bounded operator from X into Y is completely compact and Z is a completely complemented subspace of X ⊕ Y , then there exists a completely bounded automorphism τ : X ⊕ Y → X ⊕ Y with completely bounded inverse such that τZ = X0 ⊕ Y0, where X0 and Y0 are completely complemented subspaces of X and Y , respectively. If X and Y...

In this paper we study the concept of Fuzzy-anti-n-normed linear operator as a generalization of Fuzzy-anti-2normed linear operator. Fuzzy-anti-n-continuous linear operator and three types (strongly, weakly, and sequentially) of Fuzzy-anti-n-continuous linear operators are defined and relation between strongly, weakly and sequentially Fuzzy-anti-n-continuous linear operator is developed. Also s...