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The C * -algebra of a Hilbert bimodule

Sergio Doplicher, Claudia Pinzari, Rita Zuccante (1998)

Bollettino dell'Unione Matematica Italiana

Un C * -modulo hilbertiano destro X su una C * -algebra A dotato di uno * -omomorfismo isometrico ϕ : A → L A ⁢ X viene qui considerato come un oggetto X A della C * -categoria degli A -moduli Hilbertiani destri. Come in [11], associamo ad esso una C * -algebra O X A contenente X come un « A -bimodulo hilbertiano in O X A ». Se X è pieno e proiettivo finito O X A è la C * -algebra C * ⁢ X , la generalizzazione delle algebre di Cuntz-Krieger introdotta da Pimsner [27] (e in un caso particolare da Katayama [31]). Più in generale, C * ⁢ X è canonicamente immersa...

The C k Space

Katuhiko Kanazashi, Hiroyuki Okazaki, Yasunari Shidama (2013)

Formalized Mathematics

In this article, we formalize continuous differentiability of realvalued functions on n-dimensional real normed linear spaces. Next, we give a definition of the Ck space according to [23].

The Campanato, Morrey and Hölder spaces on spaces of homogeneous type

Eiichi Nakai (2006)

Studia Mathematica

We investigate the relations between the Campanato, Morrey and Hölder spaces on spaces of homogeneous type and extend the results of Campanato, Mayers, and Macías and Segovia. The results are new even for the ℝⁿ case. Let (X,d,μ) be a space of homogeneous type and (X,δ,μ) its normalized space in the sense of Macías and Segovia. We also study the relations of these function spaces for (X,d,μ) and for (X,δ,μ). Using these relations, we can show that theorems for the Campanato, Morrey or Hölder spaces...

The canonical test case for the non-commutative Singer-Wermer conjecture

Marc P. Thomas (2009)

Studia Mathematica

It is a famous conjecture that every derivation on each Banach algebra leaves every primitive ideal of the algebra invariant. This conjecture is known to be true if, in addition, the derivation is assumed to be continuous. It is also known to be true if the algebra is commutative, in which case the derivation necessarily maps into the (Jacobson) radical. Because I. M. Singer and J. Wermer originally raised the question in 1955 for the case of commutative Banach algebras, the conjecture is...

The Cauchy-Riemann equations in infinite dimensions

László Lempert (1998)

Journées équations aux dérivées partielles

I will explain basic concepts/problems of complex analysis in infinite dimensions, and survey the few approaches that are available to solve those problems.

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