Exponential Function of a bounded Linear Operator on a Hilbert Space.

A Polynomially Bounded Operator on Hilbert Space Which Is Not Similar to a Contraction

Let ε > 0. We prove that there exists an operator Tε : `2 → `2such that for any polynomial P we have ‖P (Tε)‖ ≤ (1 +ε)‖P‖∞, but Tε isnot similar to a contraction, i.e. there does not exist an invertible operatorS : `2 → `2 such that‖S−1TεS‖ ≤ 1. This answers negatively a question at-tributed to Halmos after his well-known 1970 paper (“Ten problems in Hilbertspace”). ...

Operator Extensions on Hilbert Space

Locating the Range of an Operator on a Hilbert Space

exists (is computable) for each x in H; if P is that projection, / is the identity operator on H, and the adjoint T*ofT exists, then / P is the projection of H on ker(3*), the kernel of T*. (For an example to show that the existence of the adjoint of a bounded operator on a Hilbert space is not automatic in constructive mathematics, see Brouwerian Example 3 in [7]; see also Example 2 below.) Th...

OPERATOR THEORY ON HILBERT SPACE Class notes

A Note on Quadratic Maps for Hilbert Space Operators

In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...