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Smooth Frechet subalgebras of C ∗-algebras defined by first order differential seminorms

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Abstract

The differential structure in a C ∗-algebra defined by a dense Frechet subalgebra whose topology is defined by a sequence of differential seminorms of order 1 is investigated. This includes differential Arens–Michael decomposition, spectral invariance, closure under functional calculi as well as intrinsic spectral description. A large number of examples of such Frechet algebras are exhibited; and the smooth structure defined by an unbounded self-adjoint Hilbert space operator is discussed.

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Acknowledgements

The author thanks the referee for several suggestions that help reorganize the paper in the present form. The author gratefully acknowledge the UGC support under UGC-SAP-DRS programme F-510/3/DRS/2009 (SAP-II) to the Department of Mathematics, Sardar Patel University; as well as DST support under DST-PURSE Programme to Sardar Patel University.

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  1. SUBHASH J BHATT

    Present address: Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar, 388 120, India

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  1. Center for Interdisciplinary Studies in Science and Technology (CISST), Sardar Patel University, Vallabh Vidyanagar, 388 120, India

    SUBHASH J BHATT

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  1. SUBHASH J BHATT
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Communicating Editor: Parameswaran Sankaran

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BHATT, S.J. Smooth Frechet subalgebras of C ∗-algebras defined by first order differential seminorms. Proc Math Sci 126, 125–141 (2016). https://doi.org/10.1007/s12044-016-0265-8

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  • DOI: https://doi.org/10.1007/s12044-016-0265-8

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2000 Mathematics Subject Classification.

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