A remark on a Banach-Steinhaus theorem of Narang
Antosik, Piotr, Swartz, Charles (1990)
Portugaliae mathematica
Similarity:
Antosik, Piotr, Swartz, Charles (1990)
Portugaliae mathematica
Similarity:
Nygaard, Olav (2002)
International Journal of Mathematics and Mathematical Sciences
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...
Şerb, Ioan (2001)
Mathematica Pannonica
Similarity:
Bertram Yood (1994)
Studia Mathematica
Similarity:
Let C(Ω) be the algebra of all complex-valued continuous functions on a topological space Ω where C(Ω) contains unbounded functions. First it is shown that C(Ω) cannot have a Banach algebra norm. Then it is shown that, for certain Ω, C(Ω) cannot possess an (incomplete) normed algebra norm. In particular, this is so for where ℝ is the reals.
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.
Ioan Goleţ (2007)
Mathematica Slovaca
Similarity:
Beg, Ismat, Gal, Sorin (2002)
Journal of Applied Mathematics and Stochastic Analysis
Similarity:
Singh, Vinai K., Kumar, Santosh (2009)
General Mathematics
Similarity:
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...