For μ>0, we hence prove the "if" part of the proposition by exemplarily showing that sup ( r i, p i ) ∈ S i λ T B i r i − μ T p i < ∞ for i=1 as corresponding statements for i=2,…,6 follow along the same lines.
The core of the procedure just described is the following: Something is true for the natural numbers exactly when the corresponding statement holds for all simple infinities (i.e., is a semantic consequence of the Dedekind-Peano axioms).
Finally, we define recurrent domains for semigroups in Sect. 5 and provide a classification of such domains under some conditions which are generalizations of the corresponding statements of Fornaess Sibony [5] for the iterates of a single holomorphic endomorphism of (mathbb C^k,; kge 2).
A corresponding statement is true for operators T, Tn of finite rank which are not necessarily positive.
We also show that the corresponding statement holds true for the commutant of ˜π(C X)) under the assumption that a certain family of pure states of ˜π(C∗ is total.
The corresponding statement is less significant for insertions (p < 0.3) due to the small number of predicted non-conservative events in our set (6%, amounting to 9 events in our set of 151 insertions).
For example, it has been argued that a term such as 'John's walk' goes proxy for the corresponding statement 'John walked' [Geach 1965], so to say that John's walk was pleasant is just to say that John walked pleasantly.
For clarification, a corresponding statement has now been added to the respective legends.
The problem covers the corresponding statement with p-Laplacian in the principal part, for which it is sufficient to take (mu=0).
