DOI QR코드

DOI QR Code

ON THE RANGE CLOSURE OF AN ELEMENTARY OPERATOR

  • Published : 2006.11.30

Abstract

Let $A, B{\in}B(H)$ be Hilbert space contractions, and let ${\Delta}_{AB}$ be the elementary operator ${\Delta}_{AB}:X{\rightarrow}AXB-X$. A number of conditions which are equivalent to '${\Delta}_{AB}$ has closed range' are proved.

References

  1. P. Aiena and O. Monsalve, The single valued extension property and the generalized Kato decomposition property, Acta Sci. Math. (Szeged) 67 (2001), no. 3-4, 791-807
  2. J. Anderson and C. Foias, Properties which normal operators share with normal derivations and related operators, Pacific J. Math. 61 (1975), no. 2, 313-325 https://doi.org/10.2140/pjm.1975.61.313
  3. F. F. Bonsall and J. Duncan, Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras, Lond. Math. Soc. Lecture Notes Series 2, 1971
  4. F. F. Bonsall and J. Duncan, Numerical ranges II, Lond. Math. Soc. Lecture Notes Series 10, Cambridge University Press, New York-London, 1973
  5. B. P. Duggal and R. E. Harte, Range-kernel orthogonality and range closure of an elementary operator, Monatsch. Math. 143 (2004), no. 3, 179-187 https://doi.org/10.1007/s00605-003-0055-0
  6. N. Dunford and J. T. Schwartz, Linear Operators, Part I, A Wiley-Interscience Publication, New York, 1968
  7. M. R. Embry and M. Rosenblum, Spectra, tensor products, and linear operator equations, Pacific J. Math. 53 (1974), 95-107 https://doi.org/10.2140/pjm.1974.53.95
  8. H. G. Heuser, Functional Analysis, A Wiley-Interscience Publication, 1982
  9. K. B. Laursen and M. M. Neumann, An Introduction to Local Spectral Theory, Lond. Math. Soc. Monographs (N. S.) 20, Oxford Univ. Press, 2000
  10. M. Mbekhta, Generalisation de la decomposition de Kato aux operateurs paranormaux et spectraux, Glasgow Math. J. 29 (1987), no. 2, 159-175 https://doi.org/10.1017/S0017089500006807
  11. A. M. Sinclair, Eigenvalues in the boundary of the numerical range, Pacific J. Math. 35 (1970), 231-234 https://doi.org/10.2140/pjm.1970.35.231
  12. A. Turnsek, Orthogonality in $C_p$ classes, Monatsh. Math. 132 (2001), no. 4, 349-354 https://doi.org/10.1007/s006050170039

Cited by

  1. Various Notions of Orthogonality in Normed Spaces vol.33, pp.5, 2013, https://doi.org/10.1016/S0252-9602(13)60090-9