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Closedness and lower semicontinuity of positive sesquilinear forms

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Abstract

The relationship between the notion of closedness, lower semicontinuity and completeness (of a quotient) of the domain of a positive sesquilinear form defined on a subspace of a topological vector space is investigated and sufficient conditions for their equivalence are given.

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References

  1. Bongiorno, B., Trapani, C., Triolo, S.: Extensions of positive linear functionals on a Topological *-algebra., preprint DMA 347, Palermo 2009, Rocky Mountain J. Math., to appear

  2. Davies, E.B.: Spectral theory and differential operators. Cambridge: Cambridge University Press (1996)

    MATH  Google Scholar 

  3. Bellomonte, G., Trapani, C., Triolo, S.: Absolutely convergent extensions of nonclosable positive linear functionals, preprint DMA 349, Palermo 2009, Mediterranean J. Math., to appear

  4. Bratteli, O., Robinson, D.W.: Operator Algebras and Quantum Statistical Mechanics I. Berlin: Springer-Verlag (1979)

    Google Scholar 

  5. Nelson, E.: Note on non-commutative integration, J. Funct. Anal., 15 (1974) 103–116

    Article  MATH  Google Scholar 

  6. Riesz, F, Sz.-Nagy, B.: Fuctional Analysis. London: Blackie & Son, (1956)

    Google Scholar 

  7. Segal, I.E.: A noncommutative extension of abstract integration, Ann. Math., 57 (1953), 401–457

    Article  Google Scholar 

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Correspondence to Camillo Trapani.

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Bellomonte, G., Trapani, C. & Triolo, S. Closedness and lower semicontinuity of positive sesquilinear forms. Rend. Circ. Mat. Palermo 58, 265–274 (2009). https://doi.org/10.1007/s12215-009-0020-4

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  • DOI: https://doi.org/10.1007/s12215-009-0020-4

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