No abstract

In this paper, it is shown that the asymptotically normable spaces are the smallest class of Frechet spaces which contains the nuclear Kothe spaces with continuous norm, the Banach spaces and is closed under e-tensor products and sub-spaces. Again our main aim will be to construct an example of a Kothe space which is Montel, admits a continuous norm, but still is not asymptotically normable. Keywords: Asymptotically normable; Frechet space; Kothe space DOI: 10.3126/bibechana.v7i0.4043BIBECHANA 7 (2011) 39-43

The Fredholm Alternative Theorem gives the notion of bounded and continuous operator which makes a family F of elements of C[a, b] bounded and equicontinuous. A continuous operator of finite rank is completely continuous but every continuous operator is not completely continuous operator. Keywords: Arzela-Ascoli's theorem; completely continuous; equicontinuous and Fredholm alternative theorem DOI: http://dx.doi.org/10.3126/bibechana.v8i0.5700 BIBECHANA 2012; 8: 127-130