So, there exists a norm-one element (zin F_{0} (e)).
We assume from now on that a Banach space is smooth, that is, the limit exists for all norm one elements.
Then to any bounded linear map T from E(M) into a Hilbert space H corresponds a positive norm one functional f∈E(2)(M ∗ such that∀x∈E(M ∥∥T x)∥∥2⩽K2∥T∥2f(x∗x+xx∗), where E(2) denotes the 2-concavification of E and K is a universal constant.
In doing so, the African Union is slowly but surely creating a new norm, one that says that constitutions are sacrosanct and leaders must leave when they're supposed to.
Worryingly for businesses, dodgy expenses are increasingly becoming a cultural norm — one which is seriously affecting bottom lines.
I fear this abnormal weather will give way to a new norm: one of colder, harsher winters that Louisianans have never seen.
And rather than accept internal segregation as an everyday norm, one grounded in the still-prevalent belief that minority students are "cognitively inferior" (or for self-professed non-racists, that they purposely under-perform out of fear of "acting white"), Snead believed otherwise.
It is proved that if such a factor is a complemented subspace of a larger C*-algebra then there exists a projection of norm one from the larger algebra onto the smaller and a new proof of the fact that the continuous Hochschild cohomology group H2c(M, M) vanishes is also included.
We show that the extension property for pure states of a C*-subalgebra B of a C*-algebra A leads to the existence of a projection of norm one R: A→B in the case where B is liminal with Hausdorff primitive ideal space.
We also discuss existence of a projection of norm one from C∗ onto the commutant of C X).
However, if large numbers of people share a discriminatory social norm, one can see that the market will reward compliance with the norm and punish noncompliance, so there will in that case be no tendency for the market to squeeze out discriminatory behavior.
