For the product, you'll need the distributive law. Then you'll need that a constant multiple of a null sequence is null, that the product of two null sequences is null, and the sum of any finite number of …

In this paper, we establish conditions under which each positive Null almost L-weakly compact operator is Null almost M-weakly compact and conversely.

a spanning set for the range of L. And since the vectors in B1 are not scalar multiples of each other, B1 is also linearly independent, and so we see that B1 is a basis for the range of L.

Zero nullspace A is called one-to-one if 0 is the only element of its nullspace null(A) = f0g Equivalently,

null space, null T T 2 L(V; W), the null space of T, denoted null T, is the subset of V consisting of those vectors that T maps to 0:

Sep 19, 2006 · embeds into Lp for some 1 < p 2 [R]. Since Lp has an unconditional basis, every weakly null normalized sequence in X has.

proof: Given A since A(X + Y ) = AX + AY and A(aX) = a(AX) it is clear that L(X) = AX is a linear transformation. For the converse, assume L → m