We prove that given a real JB*-triple E, and a real Hilbert space H , then the set of those bounded linear operators T from E toH , such that there exists a norm one functionalφ ∈ E∗ and corresponding pre-Hilbertian semi-norm ‖.‖φ on E such that ‖T (x)‖ ≤ 4 √ 2‖T‖ ‖x‖φ for all x ∈ E, is norm dense in the set of all bounded linear operators from E toH . As a tool for the above result, we show th...

Some basic facts about Fredholm indices are briefly reviewed, often used in connection with Toeplitz and pseudodifferential operators, and which may be relevant for operators associated to fractals. Let H be a complex infinite-dimensional separable Hilbert space, which is of course unique up to isomorphism. Let B(H) be the Banach algebra of bounded linear operators on H, and let C(H) be the clo...

DAEs: Infinite-dimensional LTI Index-1 Case 3.1 Infinite-dimensional Linear Algebra We first collect some useful infinite-dimensional definitions and statements which will be used in this and the next section. Details and proofs of these statements can be found in standard functional analysis references such as [11], [26], [28] and [38]: Proposition 3.1. Let L(X,Y ) denote the space of bounded ...

We show how local estimates may be obtained for holomorphic functions of a class of linear operators on a finite-dimensional linear vector space. This is accomplished by classifying the spectrum of each operator and then estimating its resolvent on certain contours in the left half-plane. We apply these methods to prove some known theorems, and in addition we obtain new estimates for the invers...

For a nite system A of bounded linear operators whose real linear combinations have real spectrum, the monogenic functional calculus is used to associate a function f(A) of the operators with any analytic function f in n real variables deened in a neighbourhood of the monogenic spectrum (A). Here, the existence of projection operators that decompose the functional calculus onto invariant subspa...

Dedicated to Professor Shmuel Friedland. Abstract Let B(H) be the algebra of bounded linear operator acting on a Hilbert space H (over the complex or real field). Characterization is given to A1, . . . , Ak ∈ B(H) such that for any unitary operators U1, . . . , Uk, ∑k j=1 U ∗ j AjUj is always in a special class S of operators such as normal operators, self-adjoint operators, unitary operators. ...