Displaying similar documents to “ K W does not imply K W * .”

On cyclic α(·)-monotone multifunctions

S. Rolewicz (2000)

Studia Mathematica

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Let (X,d) be a metric space. Let Φ be a linear family of real-valued functions defined on X. Let Γ : X 2 Φ be a maximal cyclic α(·)-monotone multifunction with non-empty values. We give a sufficient condition on α(·) and Φ for the following generalization of the Rockafellar theorem to hold. There is a function f on X, weakly Φ-convex with modulus α(·), such that Γ is the weak Φ-subdifferential of f with modulus α(·), Γ ( x ) = Φ - α f | x .

Subnormal operators, cyclic vectors and reductivity

Béla Nagy (2013)

Studia Mathematica

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Two characterizations of the reductivity of a cyclic normal operator in Hilbert space are proved: the equality of the sets of cyclic and *-cyclic vectors, and the equality L²(μ) = P²(μ) for every measure μ equivalent to the scalar-valued spectral measure of the operator. A cyclic subnormal operator is reductive if and only if the first condition is satisfied. Several consequences are also presented.