Displaying similar documents to “The adjoint theorem on A-spaces.”

On the lambda-property and computation of the lambda-function of some normed spaces.

Mohamed Akkouchi, Hassan Sadiky (1993)

Extracta Mathematicae


R. M. Aron and R. H. Lohman introduced, in [1], the notion of lambda-property in a normed space and calculated the lambda-function for some classical normed spaces. In this paper we give some more general remarks on this lambda-property and compute the lambda-function of other normed spaces, namely: B(S,∑,X) and M(E).

Banach’s Continuous Inverse Theorem and Closed Graph Theorem

Hideki Sakurai, Hiroyuki Okazaki, Yasunari Shidama (2012)

Formalized Mathematics


In this article we formalize one of the most important theorems of linear operator theory - the Closed Graph Theorem commonly used in a standard text book such as [10] in Chapter 24.3. It states that a surjective closed linear operator between Banach spaces is bounded.

On (a,b,c,d)-orthogonality in normed linear spaces

C.-S. Lin (2005)

Colloquium Mathematicae


We first introduce a notion of (a,b,c,d)-orthogonality in a normed linear space, which is a natural generalization of the classical isosceles and Pythagorean orthogonalities, and well known α- and (α,β)-orthogonalities. Then we characterize inner product spaces in several ways, among others, in terms of one orthogonality implying another orthogonality.

Bidual Spaces and Reflexivity of Real Normed Spaces

Keiko Narita, Noboru Endou, Yasunari Shidama (2014)

Formalized Mathematics


In this article, we considered bidual spaces and reflexivity of real normed spaces. At first we proved some corollaries applying Hahn-Banach theorem and showed related theorems. In the second section, we proved the norm of dual spaces and defined the natural mapping, from real normed spaces to bidual spaces. We also proved some properties of this mapping. Next, we defined real normed space of R, real number spaces as real normed spaces and proved related theorems. We can regard linear...