Directedness in Ordered Normed Spaces and Operators.
Kung-Fu Ng, Michel Duhoux (1981)
Mathematische Annalen
Similarity:
Kung-Fu Ng, Michel Duhoux (1981)
Mathematische Annalen
Similarity:
Keiko Narita, Noboru Endou, Yasunari Shidama (2014)
Formalized Mathematics
Similarity:
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...
Makeev, V.V. (2005)
Journal of Mathematical Sciences (New York)
Similarity:
C.-S. Lin (2005)
Colloquium Mathematicae
Similarity:
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.
Kazuhisa Nakasho, Noboru Endou (2015)
Formalized Mathematics
Similarity:
In this article, the separability of real normed spaces and its properties are mainly formalized. In the first section, it is proved that a real normed subspace is separable if it is generated by a countable subset. We used here the fact that the rational numbers form a dense subset of the real numbers. In the second section, the basic properties of the separable normed spaces are discussed. It is applied to isomorphic spaces via bounded linear operators and double dual spaces. In the...
Singh, Vinai K., Kumar, Santosh (2009)
General Mathematics
Similarity:
Alonso, Javier (1992)
International Journal of Mathematics and Mathematical Sciences
Similarity:
Ioan Goleţ (2007)
Mathematica Slovaca
Similarity:
Hideki Sakurai, Hiroyuki Okazaki, Yasunari Shidama (2012)
Formalized Mathematics
Similarity:
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.