Projective spectrum and kernel bundle

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• 作者：Wei He ; RongWei Yang
• 关键词：projective spectrum ; domain of holomorphy ; Clifford algebra ; kernel bundle ; Chern character
• 刊名：SCIENCE CHINA Mathematics
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：58
• 期：11
• 页码：2363-2372
• 全文大小：195 KB
• 参考文献：1.Andersson M, Sjöstrand J. Functional calculus for non-commuting operators with real spectra via an iterated Cauchy formula. J Funct Anal, 2004, 210: 341–375MathSciNet CrossRef MATH
  2.Atkinson F V. Multiparameter Eigenvalue Problems. Volume I: Matrices and Compact Operators. New York-London: Academic Press, 1972MATH
  3.Bannon J P, Cade P, Yang R. On the spectrum of Banach algebra-valued entire functions. Illinois J Math, 2011, 55: 1455–1465MathSciNet MATH
  4.Cade P, Yang R. Projective spectrum and cyclic cohomology. J Funct Anal, 2013, 265: 1916–1933MathSciNet CrossRef MATH
  5.Chagouel I, Stessin M, Zhu K. Geometric spectral theory for compact operators. ArXiv:1309.4375v1, 2013
  6.Feynman R. An operator calculus having applications in quantum electrodynamics. Phys Rev, 1951, 84: 108–128MathSciNet CrossRef MATH
  7.Hartshorne R. Algebraic Geometry. New York-Heidelberg: Springer, 1977CrossRef MATH
  8.Jefferies B. Spectral Properties of Noncommuting Operators. Berlin: Springer-Verlag, 2004MATH
  9.Krantz S G. Function Theory of Several Complex Variables. Providence, RI: Amer Math Soc Chelsea Publishing, 2001MATH
  10.Marcus A, Spielman D, Srivastava N. Interlacing families II: Mixed characteristic polynomials and the Kadison-Singer problem. ArXiv:1306.3969v4, 2014MATH
  11.Rudin W. Functional Analysis, 2nd ed. New York: McGraw-Hill, 1991MATH
  12.Shirikov D. Concepts of trace, determinant and inverse of Clifford algebra elements. ArXiv:1108.5447v1, 2011
  13.Sleeman B D. Multiparameter Spectral Theory in Hilbert Space. Boston-London: Pitman, 1978MATH
  14.Stessin M, Yang R, Zhu K. Analyticity of a joint spectrum and a multivariable analytic Fredholm theorem. New York J Math, 2011, 17: 39–44MathSciNet MATH
  15.Taylor J. A joint spectrum for several commuting operators. J Funct Anal, 1970, 6: 172–191CrossRef MathSciNet MATH
  16.Vinnikov V. Complete description of determinantal representations of smooth irreducible curves. Linear Algebra Appl, 1989, 125: 103–140MathSciNet CrossRef MATH
  17.Weyl H. The Theory of Groups and Quantum Mechanics. New York: Dover, 1950MATH
  18.Yang R. Projective spectrum in Banach algebras. J Topol Anal, 2009, 1: 289–306MathSciNet CrossRef MATH
  
• 作者单位：Wei He (1)
  RongWei Yang (2)
  
  1. Department of Mathematics, Southeast University, Nanjing, 211189, China
  2. Department of Mathematics and Statistics, The State University of New York, Albany, NY, 12222, USA
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Chinese Library of Science
  Applications of Mathematics
  
• 出版者：Science China Press, co-published with Springer
• ISSN：1869-1862

文摘

For a tuple A = (A ₁,A ₂, …,A _n ) of elements in a unital algebra B over ℂ, its projective spectrum P(A) or p(A) is the collection of z ∈ ℂ ^{n , or respectively z ∈ ℙ n−1, such that A(z) = z ₁ A ₁+z ₂ A ₂+…+z _n A _n is not invertible in B. The first half of this paper proves that if B is Banach then the resolvent set P c (A) consists of domains of holomorphy. The second half computes the projective spectrum for the generating vectors of a Clifford algebra. The Chern character of an associated kernel bundle is shown to be nontrivial.}