Dissertation > Excellent graduate degree dissertation topics show

The Map Preserving the Lattices of Invariant Subspaces and Centralizers on Operator Algebras

Author: FengMin
Tutor: ZhangJianHua
School: Shaanxi Normal University
Course: Basic mathematics
Keywords: Upper triangular matrix algebra Standard operator algebras Finite rank operator algebra Self-adjoint operator algebras Invariant subspace lattice Centralizers Additive Maps
CLC: O177.1
Type: Master's thesis
Year: 2010
Downloads: 17
Quote: 0
Read: Download Dissertation

Abstract


The operator algebra theory in the 1930s , with the rapid development of this theory , this theory has now become a popular branch of modern mathematics . Quantum mechanics , non-commutative geometry , linear systems , control theory , number theory , as well as some other important branches of mathematics has unexpected ties and mutual penetration in order to further deepen the knowledge and understanding of the operator algebra , in recent years , more and more attention on the operator algebra mapping characterizations problem which including linear preserver the centralizer , derivation , and found that many of the novel method of proof , and continue to put forward new ideas , such as alternating maps , the introduction of the concept of function identities , these mapping has become a study operator algebras indispensable tool in this article has been concluded on the basis of the main upper triangular matrix algebra Paul invariant subspace lattice mapping , standard operator algebras and finite rank operator algebras on several identities depicted in this article points three chapters , as follows : the first chapter introduces some of the symbols to be used in this article , the definition , as well as to be used herein known conclusions and theorems first section , we introduce the upper triangular matrix algebra , the standard operator algebra, self-adjoint operator algebra , finite rank operator algebra concepts . Section II introduces Paul invariant subspace lattice mapping the prime ring centralizers concept III introduces some of the well-known theorem . two chapters mainly on the protection on the upper triangular matrix algebra Tn invariant subspace lattice mapping Φ depicted . portray such mapping specific form , in the form of Φ Φ ( a ) = αA φ (A ) I. operator a ∈ Tn , α ∈ F, φ : Tn → F. we first standard on operator algebras a centralizers depicted , proved to meet 2Φ ( an )- Φ ( a ) An - AnΦ ( a ) ∈ FI (st ) Φ (A3 ) - sΦ ( A2 ) a - tAΦ ( A2 ) ∈ FI the mapping Φ centralizers ; followed by a discussion of finite rank operator algebra F (X ) meet 2Φ (Am n) = Φ (Am) An AnΦ (Am) or Φ (An 1 ) = SΦ ( An ) the A tAΦ ( AN ) of the mapping Φ has the form : Φ (A ) (st) = λA where λ is a fixed constant .

Related Dissertations

  1. Characterizations of Derivations, Centralizers and Some Other Mappings on Operator Algebras,O153.3
  2. Jordan Isomorphism and Elementary on Operator Algebras,O177
  3. Research on Additive Mapping Preserving Anti-orthogonality and Preserving Commutative Zero-product,O177
  4. Additive Maps Preserving Rank 1 Hermite matrix space,O151.21
  5. Several types of hybrid stochastic stability of functional equations,O177
  6. Derivations and Centralizers on Prime and Semiprime Rings,O153.3
  7. On Some Unsolved Problems of Finite p-groups,O152.1
  8. Jordan derivations on operator algebras and Jordan map,O153.3
  9. Preserving Problems between Matrix Spaces,O151.21
  10. M-P inverse Additive Maps Preserving,O151.21
  11. Generalized Jordan Derivation and Generalized Antiderivation on a Triangular Matrix Algebra,O177
  12. Centralizers, (α,β)-derivations and Anti-isomorphisms on J-subspace Lattice Algebras,O177
  13. The Centralizers of Nest Algebras,O153
  14. Types of intuitionistic fuzzy hybrid functional equation stability,O177.91
  15. A class of functional equations and the stability of functional inequalities,O177.91
  16. On Core-finite and Its Dual Problems,O152
  17. Inverse-Preserving Additive Maps on Hermitian Matrix Spaces,O151.21
  18. Centralizers on the sets of algebra and higher order Lie derivation,O177.1
  19. The Arithmetical Conditions of Conjugacy Classes and the Structures of Finite Groups,O152.1
  20. E ( n ) - Azumaya algebra structure,O152.1

CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Functional Analysis > Hilbert space and linear operator theory
© 2012 www.DissertationTopic.Net  Mobile