Some theorems on the generalized numerical ranges

References

• Au-Yeung , Y.H. 1969 . A theorem on a mapping from a sphere to the circle and the simultaneous diagonalization of two hermitian matrices . Proc. Amer. Math. Soc. , 20 : 545 – 548 .
   Web of Science ®Google Scholar
• Au-Yeung , Y.H. 1975 . A simple proof of the convexity of the field of values defined by two hermitian forms . Aequations Math. , 12 : 82 – 83 .
   Google Scholar
• Berger , C.A. 1963 . Normal dilations , Cornell University . Doctoral dissertation
   Google Scholar
• Birkhoff , G. 1946 . Tres observaciones sobre ei algebra lineal . Univ. Nac. Tucuman Rev. Ser. A. , 5 : 147 – 150 .
   Google Scholar
• Brickman , L. 1961 . On the field of values of a matrix . Proc. Amer. Math. Soc. , 12 : 61 – 66 .
   Google Scholar
• Calabi , E. 1964 . Linear systems of real quadratic forms . Proc. Amer. Math. Soc. , 15 : 844 – 846 .
   Google Scholar
• Fan , K. 1950 . “ On a theorem of Weyl concerning eigenvalues of linear transformations ” . In Proc. Nat. Acad. Sci. Vol. II , 31 – 35 . U.S.A.
   Google Scholar
• Fillmore , P.A. and Williams , J.P. 1971 . Some convexity theorems for matrices . Glasgow Math. J. , 12 : 110 – 117 .
   Web of Science ®Google Scholar
• Finsler , P. 1936/37 . Über das vorkommen definiter und semidefiniter formen in Scharen quadratischer formen . Comment. Math. Helv. , 9 : 188 – 192 .
   Google Scholar
• Goldberg and Straus , E.G. 1976 . Inclusion relations involving k-numerical ranges . Linear Algebra and Appl. , 15 : 261 – 270 .
   Web of Science ®Google Scholar
• Goldberg , M. and Straus , E.G. 1977 . Elementary inclusion relations for generalized numerical ranges . Linear Algebra and Appl. , 18 : 1 – 24 .
   Web of Science ®Google Scholar
• Halmos , P. 1967 . A Hilbert Space Problem Book , New York : Van Nostrand .
   Google Scholar
• Hausdorff , F. 1919 . Der Wertvorrat einer Bilinearform . Math. Z. , 3 : 314 – 316 .
   Google Scholar
• Hestenes , M.R. 1968 . Pairs of quadratic forms . Linear Algebra and Appl. , 1 : 397 – 407 .
   Google Scholar
• Horn , A. 1954 . Doubly stochastic matrices and the diagonal of a rotational matrix . Amer. J. Math. , 76 : 620 – 630 .
   Google Scholar
• Marcus , M. 1979 . Some combinatorial aspects of numerical range . Ann. New York Acad. Sci. , 76 : 368 – 376 .
   Google Scholar
• Mclntosh , A. 1978 . The Toeplitz-hausdorff theorem and ellipticity conditions . Amer. Math. Monthly , 85 ( 6 ) : 475 – 477 .
   Web of Science ®Google Scholar
• Poon , Y. T. 1980 . Another proof of a result of westwick . Linear and Multilinear Algebra , 9 ( 6 ) : 35 – 37 .
   Google Scholar
• Rudin , W. 1973 . Functional Analysis , New York : McGraw-Hill, Inc. .
   Google Scholar
• Toeplitz , O. 1918 . Das algebraishe analogon zu einem Satze von Fejér . Math. Z. , 2 : 187 – 197 .
   Google Scholar
• Uhlig , F. 1979 . A recurring theorem about pairs of quadratic forms and extensions:A survey . Linear Algebra and Appl. , 25 : 219 – 237 .
   Web of Science ®Google Scholar
• Westwick , R. 1975 . A theorem on numerical ranges . Linear and Multilinear Algebra , 2 : 311 – 315 .
   Google Scholar