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Inner-outer factorization of operator-valued functions on ordered groups

Mihály Bakonyi, Dan Timotin (2005)

Studia Mathematica

Inner-outer factorization for matrix-valued functions defined on totally ordered groups has been considered by Helson and Lowdenslager in connection with multivariate prediction theory. We discuss their result in an operator-theoretic framework and prove that there are obstructions to its extension to operator-valued functions.

Integral formulae for special cases of Taylor's functional calculus

D. Albrecht (1993)

Studia Mathematica

In this paper integral formulae, based on Taylor's functional calculus for several operators, are found. Special cases of these formulae include those of Vasilescu and Janas, and an integral formula for commuting operators with real spectra.

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