203
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Spectra, norms and numerical ranges of generalized quadratic operators

, &
Pages 1077-1104 | Received 18 Jan 2010, Accepted 02 Apr 2010, Published online: 23 Sep 2011

References

  • Anderson , J and Stampfli , JG . 1971 . Commutators and compressions . Israel J. Math. , 10 : 433 – 441 .
  • Au-Yeung , YH and Tsing , NK . 1983 . A conjecture of Marcus on the generalized numerical range . Linear Multilinear Algebra , 14 : 235 – 239 .
  • Chien , MT , Tso , SH and Wu , PY . 2003 . Higher-dimensional numerical ranges of quadratic operators . J. Operator Theory , 49 : 153 – 171 .
  • Choi , MD , Holbrook , JA , Kribs , DW and Życzkowski , K . 2007 . Higher-rank numerical ranges of unitary and normal matrices . Oper. Matrices , 1 : 409 – 426 .
  • Choi , MD , Kribs , DW and Życzkowski , K . 2006 . Higher-rank numerical ranges and compression problems . Linear Algebra Appl. , 418 : 828 – 839 .
  • Choi , MD , Kribs , DW and Życzkowski , K . 2006 . Quantum error correcting codes from the compression formalism . Rep. Math. Phys. , 58 : 77 – 91 .
  • Choi , MD and Li , CK . 2000 . Numerical ranges and dilations . Linear Multilinear Algebra , 47 : 35 – 48 .
  • Choi , MD and Li , CK . 2004 . Norm bounds for summation of two normal matrices . Linear Algebra Appl. , 379 : 137 – 157 .
  • Choi , MD and Li , CK . 2006 . The ultimate estimate of the upper norm bound for the summation of operators . J. Funct. Anal. , 232 : 455 – 476 .
  • Davis , C . 1968 . The shell of a Hilbert-space operator . Acta Sci. Math. (Szeged) , 29 : 69 – 86 .
  • Davis , C . 1970 . The shell of a Hilbert-space operator: II . Acta Sci. Math. (Szeged) , 31 : 301 – 318 .
  • Furuta , T . 2008 . Applications of polar decompositions of idempotent and 2-nilpotent operators . Linear Multilinear Algebra , 56 : 69 – 79 .
  • Garcia , SR . 2008 . Approximate antilinear eigenvalue problems and related inequalities . Proc. Amer. Math. Soc. , 136 : 171 – 179 .
  • Gustafson , KE and Rao , DKM . 1997 . Numerical Range: The Field of Values of Linear Operators and Matrices , New York : Universitext, Springer-Verlag .
  • Halmos , P . 1982 . A Hilbert Space Problem Book, 2nd ed. Graduate Texts in Mathematics, Vol. 19, Encyclopedia of Mathematics and its Applications , New York : Springer-Verlag .
  • Horn , RA and Johnson , CR . 1991 . Topics in Matrix Analysis , Cambridge : Cambridge University Press .
  • Li , CK . 1996 . A simple proof of the elliptical range theorem . Proc. Am. Math. Soc. , 124 : 1985 – 1986 .
  • Li , CK and Nakazato , H . 1998 . Some results on the q-numerical ranges . Linear Multilinear Algebra , 43 : 385 – 410 .
  • Li , CK , Poon , YT and Sze , NS . 2008 . Higher rank numerical ranges and low rank perturbation of quantum channels . J. Math. Anal. Appl. , 348 : 843 – 855 .
  • Li , CK , Poon , YT and Sze , NS . 2009 . Condition for the higher rank numerical range to be non-empty . Linear Multilinear Algebra , 57 : 365 – 368 .
  • Li , CK , Poon , YT and Sze , NS . Elliptical range theorems for generalized numerical ranges of quadratic operators . preprint, Rocky Mountain J. Math. , (to appear). Available at http://www.people.wm.edu/~cklixx/quadra.pdf
  • Li , CK and Sze , NS . 2008 . Canonical forms, higher rank numerical ranges, totally isotropic subspaces, and matrix equations . Proc. Amer. Math. Soc. , 136 : 3013 – 3023 .
  • Marcus , M . Some combinatorial aspects of numerical range, Second International Conference on Combinatorial Mathematics, Ann. New York Acad. Sci., 319 (1979), pp. 368–376
  • Martinez-Avendano , RA . 2008 . Higher-rank numerical range of operators in infinite-dimensional Hilbert space . Oper. Matrices , 2 : 249 – 264 .
  • Pietsch , A . 1987 . Eigenvalues and s-Numbers , Cambridge : Cambridge University Press .
  • Rodman , L and Spitkovsky , I . 2008 . On generalized numerical ranges of quadratic operators . Oper. Theory Adv. Appl. , 179 : 241 – 256 .
  • Tsing , NK . 1984 . The constrained bilinear form and the C-numerical range . Linear Algebra Appl. , 56 : 195 – 206 .
  • Tso , S-H and Wu , PY . 1999 . Matricial ranges of quadratic operators . Rocky Mountain J. Math. , 29 : 1139 – 1152 .
  • Wielandt , H . 1955 . On eigenvalues of sums of normal matrices . Pac. J. Math. , 5 : 633 – 638 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.