Sentence examples for be the weak closure from inspiring English sources

Let be the weak closure of.

Let K be a compact subset of the complex plane C, and let μ be a finite, positive Borel measure on K. Define R∞ to be the weak-star closure in L∞ of the algebra of rational functions with poles off K. For f ϵ R∞, we consider A∞ f, μ), the weak-star closure in L∞ of the algebra generated by R∞ and the complex conjugate f of f.

Let f be a function of semigroup into a reflexive Banach space such that the weak closure of is weakly compact, and let be a subspace of containing all functions with.

As a consequence, it is shown that if B is an arbitrary bounded Boolean algebra of bounded projections on a Banach space X, then AlgLat B) is the weak operator topology closure of the linear span of B. These generalize the work of several authors.

Let be a function of a semigroup into such that the weak closure of is weakly compact.

Note that (the weak closure of ) is a weakly closed subset of for each.

Here is a multivalued operator and denotes the weak closure of the set.

We denote as the weak closure of, that is, if there exists a sequence such that for every.

We denote (bar{E}^{w}) as the weak closure of E, that is, (xinbar{E}^{w}), if there exists a sequence ({x_{n}}subset E ) such that (f(x_{n})rightarrow f(x) ) for every (fin X^).

We denote (overline{E}^{omega}) as the weak closure of E, that is, (uin overline{E}^{omega}) if there exists a sequence ({u_{n}}subset E) such that (g u_{n} to g u)) for every (gin X^).

Consequently the weak closure of any masa bimodule of trace class operators is strongly reflexive.