Displaying similar documents to “Decomposition of operators with countable spectrum.”

Weighted shift operators on l spaces.

Lucas Jódar (1986)

Stochastica

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The analytic-spectral structure of the commutant of a weighted shift operator defined on a l space (1 ≤ p < ∞) is studied. The cases unilateral, bilateral and quasinilpotent are treated. We apply the results to study certain questions related to unicellularity, strictly cyclicity and the existence of hyperinvariant subspaces.

Some results about absolute summability of operators in Banach spaces.

Luis López Corral (1986)

Stochastica

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In order to study the absolute summability of an operator T we consider the set S = {{x} | ∑||Tx|| < ∞}. It is well known that an operator T in a Hilbert space is nuclear if and only if S contains an orthonormal basis and it is natural to ask under which conditions two orthonormal basis define the same left ideal of nuclear operators. Using results about S we solve this problem in the more general context of Banach spaces.

Some remarks on a problem of C. Alsina.

J. Matkowski, M. Sablik (1986)

Stochastica

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Equation [1] f(x+y) + f (f(x)+f(y)) = f (f(x+f(y)) + f(f(x)+y)) has been proposed by C. Alsina in the class of continuous and decreasing involutions of (0,+∞). General solution of [1] is not known yet. Nevertheless we give solutions of the following equations which may be derived from [1]: [2] f(x+1) + f (f(x)+1) = 1, [3] f(2x) + f(2f(x)) = f(2f(x + f(x))). Equation [3] leads to a Cauchy functional equation: ...

On the extension of Rosenbrock's theory in algebraic design on multivariable controllers.

Manuel de la Sen (1986)

Stochastica

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System similarity and system strict equivalence concepts from Rosenbrock's theory on linear systems are used to establish algebraic conditions of model matching as well as an algebraic method for design of centralized compensators. The ideas seem to be extensible without difficulty to a class of decentralized control.

Representation of continuous associative functions.

Barbara Baccheli (1986)

Stochastica

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Strengthened forms of Ling's representation theorem concerning a class of continuous associative functions are given: Firstly the monotonicity condition is removed. Then the associativity condition is replaced by the power associativity.