Abstract
Main developments in the field of hyponormal operators are due to a few specific inequalities. The oldest and best known inequality was discovered by Putnam [18]. Then, Berger and Shaw [4] obtained a sharper inequality. Afterwards, a few estimates of an intrinsic object attached to certain hyponormal opertors, namely the principal function, turned out to be the finest quantitative results.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ahlfors, L; Beurling, A.: Conformal invariants and function theoretic null sets, Acta Math. 83(1950), 101–129.
Alexander, H.: Projections of polynomial hulls, J.Funct.Anal. 13(1973), 13–19.
Axler,S.; Shapiro,J.H.: Putnam′s theorem, Alexander′s spectral area estimate, and VMO, Math. Ann. 271(1985), 161–183.
Berger, C.A.; Shaw, B.I.: Self-commutators of multicyclic hyponormal operators are always trace class,Bull. Amer. Math. Soc. 79(1973), 1193–1199.
Carey, R.W.; Pineus, J.D.: Commutators, symbols and determining functions, J. Funct. Anal. 19(1975), 50–80.
Carey, R.W.; Pincus, J. D.: An integrality theorem for subnormal operators, Integral Equations Operator Theory 4(1981), 10–44.
Clancey, K.F.: Seminormal operators, Lecture Notes in Math., No.742, Springer, Berlin—Heidelberg—New York, 1979.
Clancey, K.F.: A kernel for operators with one-dimensional self-commutator, Integral Equations Operator Theory 7(1984), 441–458.
Clancey, K.F.: Hilbert space operators with one-dimensional self-commutator, J. Operator Theory 13(1985), 265–289.
Clancey, K.F.: The Cauchy transform of the principal function associated with a non-normal operator,Indiana Univ. Math. J. 34(1985), 21–32.
Conway, J.B.; Putnam, C.R.: An irreducible subnormal operator with infinite multiplicities, J. Operator Theory 13(1985), 291–297.
Helton, J.W.; Howe, R.: Integral operators, commutator traces, index and homology, in Lecture Notes in Math., Nr.345, Springer, Berlin—Heidelberg—New York, 1973, pp.141–209.
Martin, M.; Putinar, M.: A unitary invariant for hyponormal operators, J, Funct. Anal. 73(1987), 297–323.
Morrel, B.B.: A decomposition for some operators, Indiana Univ. Math. J. 23(1973), 497–511.
Pincus, J.D.: Commutators and systems of singular integral equations. I, Acta Math. 121(1968), 219–249.
Pincus, J.D.; Xia, Daoxing; Xia, Jingbo: The analytic model of a hyponormal operator with rank one self-commutator, Integral Equations Operator Theory 7(1984), 516–535.
Putinar, M.: Extensions scalaires et noyaux distribution des opérateurs hyponormaux, C. R. Acad. Sci. Paris 301, série I, nr.15(1985), 739–741.
Putnam, C.R.: An inequality for the area of hyponormal spectra, Math. Z. 116(1970), 323–330.
Putnam, C.R.: Resolvent vectors, invariant subspaces and sets of zero capacity, Math. Ann. 205(1973), 165–171.
Putnam, C.R.: Hyponormal operators and spectral multiplicity, Indiana Univ. Math. J. 28(1979), 701–709.
Voiculescu, D.: A note on quasitriangularity and trace-class self-commutators, Acta Sci. Math. (Szeged) 42(1980), 195–199.
Xia, Daoxing: On the kernels associated with a class of hyponormal operators, Integral Equations Operator Theory 6(1983), 444–452.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Birkhäuser Verlag Basel
About this chapter
Cite this chapter
Putinar, M. (1988). Extreme Hyponormal Operators. In: Arsene, G. (eds) Special Classes of Linear Operators and Other Topics. Operator Theory: Advances and Applications, vol 28. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9164-6_18
Download citation
DOI: https://doi.org/10.1007/978-3-0348-9164-6_18
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-1970-0
Online ISBN: 978-3-0348-9164-6
eBook Packages: Springer Book Archive