Proof Theory of Riesz Spaces and Modal Riesz Spaces

Pointfree Spectra of Riesz Spaces

One of the best ways of studying ordered algebraic structures is through their spectra. The three well-known spectra usually considered are the Brumfiel, Keimel, and the maximal spectra. The pointfree versions of these spectra were studied by B. Banaschewski for f -rings. Here, we give the pointfree versions of the Keimel and the maximal spectra for Riesz spaces. Moreover, we briefly mention ho...

Integral and ideals in Riesz spaces

A convergence in Riesz spaces is given axiomatically. A Bochner-type integral for Riesz space-valued functions is introduced and some Vitali and Lebesgue dominated convergence theorems are proved. Some properties and examples are investigated. A.M.S. SUBJECT CLASSIFICATION (2000): 28B15.

Riesz Bases in Sobolev Spaces 1792 Hb

Riesz Theorems in 2-inner Product Spaces

In this paper we describe the proof of ’Riesz Theorems’ in 2inner product spaces. The main result holds only for a b-linear functional but not for a bilinear functional. AMS Mathematics Subject Classification (2010): 41A65, 41A15

Compact operators on Banach spaces: Fredholm-Riesz

1. Compact operators on Banach spaces 2. Appendix: total boundedness and Arzela-Ascoli [Fredholm 1900/1903] treated compact operators as limiting cases of finite-rank operators. [1] [Riesz 1917] defined and made direct use of the compactness condition, more apt for Banach spaces. See [Riesz-Nagy 1952] for extensive discussion in the Hilbert-space situation, and many references to original paper...