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Isolated points of some sets of bounded cosine families, bounded semigroups, and bounded groups on a Banach space

Adam Bobrowski, Wojciech Chojnacki (2013)

Studia Mathematica

We show that if the set of all bounded strongly continuous cosine families on a Banach space X is treated as a metric space under the metric of the uniform convergence associated with the operator norm on the space 𝓛(X) of all bounded linear operators on X, then the isolated points of this set are precisely the scalar cosine families. By definition, a scalar cosine family is a cosine family whose members are all scalar multiples of the identity operator. We also show that if the sets of all bounded...

Isomorphic random Bernoulli shifts

V. Gundlach, G. Ochs (2000)

Colloquium Mathematicae

We develop a relative isomorphism theory for random Bernoulli shifts by showing that any random Bernoulli shifts are relatively isomorphic if and only if they have the same fibre entropy. This allows the identification of random Bernoulli shifts with standard Bernoulli shifts.

Iterated function systems with continuous place dependent probabilities.

Jaroszewska, Joanna (2002)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

Iterates and the boundary behavior of the Berezin transform

Jonathan Arazy, Miroslav Engliš (2001)

Annales de l’institut Fourier

Let $μ$ be a measure on a domain $Ω$ in $ℂ^{n}$ such that the Bergman space of holomorphic functions in $L^{2} (Ω, μ)$ possesses a reproducing kernel $K (x, y)$ and $K (x, x) > 0$ $\forall x \in Ω$ . The Berezin transform associated to $μ$ is the integral...

Iteration of random-valued functions on the unit interval

Karol Baron, Marek Kuczma (1977)

Colloquium Mathematicae

Itô formula and local time for the fractional Brownian sheet.

Tudor, Ciprian A., Viens, Frederi G. (2003)

Electronic Journal of Probability [electronic only]