Sentence examples for minimal projection from inspiring English sources

First, let ℳ have no minimal projection.

Only flares that occurred within 30° from the limb were considered, so that the speed and width measurements of CMEs were subject to minimal projection effects.

Let ℳ have no minimal projection, then the associate space (Lambda_{omega}^{p} (mathcal{M})^{prime}) is a noncommutative Banach function space.

A group is said to an [AU]-group if the von Neumann algebra generated by every continuous unitary representation of is atomic (i.e., every nonzero projection in the van Neumann algebra majorizes a nonzero minimal projection).

Let ℳ have no minimal projection for every measurable function f with lim_{trightarrowinfty}d_{f}(t)=0, then there exists (xin L_{0}(mathcal{M})) such that (mu_{t}(x)=f^(t)).

Lemma 3.1 Let 0 < q < ∞, 1 ≤ p, p 0, p 1 < ∞ and p 0 ≠ p 1 such that 1 p = 1 − θ p 0 + θ p 1 for some  0 < θ < 1. Assume that ℳ has no minimal projection, then there exists a constant C such that ∀ T ∈ L p, q ( M ) we have ∥ MT ∥ p, q ≤ C ∥ T ∥ p, q. (3.1).

For matrix weights satisfying a low-pass condition we identify the minimal projections in this algebra as correlations of scaling functions, i.e., limits of cascade algorithms.

In particular, this shows that Proposition 3.1 from [H. König, N. Tomczak-Jaegermann, Norms of minimal projections, J. Funct. Anal. 119 (1994) 253 280] (see p. 259) is incorrect.

Hence the proof of the Grünbaum conjecture given in [H. König, N. Tomczak-Jaegermann, Norms of minimal projections, J. Funct. Anal. 119 (1994) 253 280] which is based on Proposition 3.1 is incomplete.

Theorem 3.2 Let 0 < q < ∞, 1 ≤ p, p 0, p 1 < ∞ and p 0 ≠ p 1 be such that 1 p = 1 − θ p 0 + θ p 1 for some  0 < θ < 1. Assume that ℳ has minimal projections, then there exists a constant C such that for all T ∈ L p, q ( M ) we have ∥ MT ∥ p, q ≤ C ∥ T ∥ p, q.

There is minimal lateral projection and the few canals that project posterior on the ventral surface are short, <1 cm (Fig. 6, sagittal plane).