Journal of Operator Theory

Volume 68, Issue 2, Fall 2012 pp. 487-500.

On orthogonal systems in Hilbert $C^*$-modules

Authors: Giovanni Landi (1) and Alexander Pavlov (2)
Author institution: (1) Dipartimento di Matematica, Universita di Trieste, Via Valerio 12/1, I-34127 Trieste, and INFN, Sezione di Trieste, Trieste, Italy
(2) Dipartimento di Matematica, Universita di Trieste, Via Valerio 12/1, I-34127 Trieste, Italy, and Department of Mathematics, All-Russian Institute of Scientific and Technical Information of Russian Academy of Sciences (VINITI RAS), Moscow, 125190 Usievicha str. 20, Russia}

Summary: Analogues for Hilbert $C^*$-modules of classical results of Fourier series theory in Hilbert spaces are considered. Relations between different properties of orthogonal and orthonormal systems for Hilbert $C^*$-modules are studied with special attention paid to the differences with the well-known Hilbert space situation.

Keywords: Orthogonal systems, Fourier series, Hilbert $C^*$-modules

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