On certain loci of Hankel r-Planes of ℙ m
We study the loci of Hankel (l + 1)-planes in ℙm containing a fixed l-plane πl. We investigate the singular locus of the variety H(r,m) of Hankel r-planes in ℙm.
Let X and Y be two inflnite dimensional real or complex Banach spaces. In this note we determine the forms of surjective additive maps ` : L(X) ! L(Y ) preserving the kernel's dimension or the range's codimension. As consequence, we establish that ` : L(X) ! L(X) preserves the kernel (respectively, the range) if and only if there exists an invertible operator A 2 L(X) such that `(T) = AT (respectively, `(T) = TA) for all T 2 L(X).