n‐Positivity of Unbounded *‐Representations

Three term recurrence relation modulo ideal and orthogonality of polynomials of several variables

“…Suppose that, contrary to our claim, there are k ∈ N such that k + 1 V , and p ∈ Q k+1 such that deg p = k + 1. Then, by (12)…”

“…Suppose (15) is valid for a fixed integer 0 k < V , and k+1 (12)). Hence, by (9) and Lemma 3 applied to Y i = V i , i = 0, .…”

“…The interested reader is referred to papers [7,12] which are in a way related to Question 1. It follows from Proposition 42 that the definitions of types A and B coincide for every p ∈ P N for which I(Z p ) = (p).…”

“…If the set B df = C \ V is linearly V-independent, then B has a column representation {Q k } V k=0 which satisfies conditions(12) and (i) of Proposition 6.Proof. Since the set B ∩ P k] N is linearly V-independent and that for every integer k 0, the set B ∩ P k] N is a V-basis of P k] N .…”

Representations of *-algebras by unbounded operators: C*-hulls, local-global principle, and induction

“…This is part of the definition of a Fell bundle over a group. For more general * -algebras, the positivity conditions for different n ∈ N in Proposition 9.5 may differ, compare [9]. Let A ⊗ Ae F be the Hilbert module completion of A Ae F for the inner product above.…”