Digital Commons Network^™

Topological Vector Spaces, Chunqing Li

Major Papers

This major paper is a report on author’s study of some topics on topological vector spaces. We prove a well-known Hahn-Banach theorem and some important consequences, including several separation and extension theorems. We study the weak topology on a topological vector space X and the weak-star topology on the dual space X* of X. We also prove the Banach-Alaoglu theorem. Consequently, we characterize the closed convex hull and the closed linear span for sets in X and X* , identify the dual of a subspace of X with the quotient of its annihilator, and obtain the Goldstine theorem as well …

Markushevich Bases And Auerbach Bases In Banach Spaces, Apala Mandal

Major Papers

This paper studies Markushevich bases and Auerbach bases in Banach spaces. Firstly, a countable 1-norming Markushevich basis is constructed for any infinite-dimensional separable Banach space. Secondly, an Auerbach basis is constructed for any finite-dimensional Banach space. Thirdly, a Markushevich basis is constructed for a class of non-separable Banach spaces by applying projectional generators and projectional resolution identities, and the transfinite induction on the density character of the space.

The Price Of Stocks, Geometric Brownian Motion, And Black Scholes Formula, Fatimah Fathalden Asiri

Major Papers

In this paper, we discuss the stock price model as Geometric Brownian motion.

After that, we obtain a closed form solution to the model using It^o's Lemma.

Moreover, we use this solution to derive the Black Scholes formula.