Two counterexamples in semigroup theory on Hilbert space

Two Counterexamples in Semigroup Theory on Hilbert Space1

There exist (C0) semigroups Tx(i), T2(t) on Hubert space with the following properties: 7f has a bounded generator and is uniformly bounded, but is not similar to a contraction semigroup. T2 is uniformly bounded, and there exists no scalar a such that e~"'T2(t) is similar to a contraction semigroup.

Elementary Hilbert Space Theory

A Hilbert Space is an inner product space that is complete. Let H be a Hilbert space and for f, g ∈ H, let 〈f, g〉 be the inner product and ‖f‖ = √ 〈f, f〉. (1.1) We will consider Hilbert spaces over C. Most arguments go through for Hilbert spaces over R, and the arguments are simpler. We assume that the reader is familiar with some of the basic facts about the inner product. Let us prove a few t...

OPERATOR THEORY ON HILBERT SPACE Class notes

Game Theory Formulated on Hilbert Space

We present a consistent formulation of quantum game theory that accommodates all possible strategies in Hilbert space. The physical content of the quantum strategy is revealed as a family of classical games representing altruistic game play supplemented by quantum interferences. Crucial role of the entanglement in quantum strategy is illustrated by an example of quantum game representing the Be...

On Minimax Theory in Two Hilbert Spaces