scholarly journals Induced map on $K$-theory for certain $\Gamma$-equivariant maps between Hilbert spaces

2021 ◽  
Author(s):  
Tsuyoshi Kato
Keyword(s):  
Hilbert Spaces ◽  
Equivariant Maps ◽  
K Theory

scholarly journals DECONSTRUCTING MONOPOLES AND INSTANTONS

2000 ◽  
Vol 12 (10) ◽  
pp. 1367-1390 ◽  
Author(s):  
GIOVANNI LANDI
Keyword(s):  
Vector Bundle ◽  
Lie Groups ◽  
Finite Type ◽  
Topological Charge ◽  
Projective Modules ◽  
Dirac Monopole ◽  
Canonical Connection ◽  
Equivariant Maps ◽  
K Theory

We give a unifying description of the Dirac monopole on the 2-sphere S2, of a graded monopole on a (2, 2)-supersphere S2, 2 and of the BPST instanton on the 4-sphere S4, by constructing a suitable global projector p via equivariant maps. This projector determines the projective modules of finite type of sections of the corresponding vector bundle. The canonical connection ∇ = p ◦ d is used to compute the topological charge which is found to be equal to -1 for the three cases. The transposed projector q = pt gives the value +1 for the charges; this showing that transposition of projectors, although an isomorphism in K-theory, is not the identity map. We also study the invariance under the action of suitable Lie groups.

An Introduction to K-Theory for C*-Algebras

2000 ◽  
Author(s):  
M. Rørdam ◽  
F. Larsen ◽  
N. Laustsen
Keyword(s):  
C Algebras ◽  
K Theory

On a question of swan in algebraic k-theory

1973 ◽  
Vol 6 (1) ◽  
pp. 85-94 ◽  
Author(s):  
Pramod K. Sharma ◽  
Jan R. Strooker
Keyword(s):  
K Theory

Unbounded Linear Operators

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Von Neumann ◽  
Limit Circle ◽  
Sectorial Operators ◽  
Closed Operators ◽  
The Stability ◽  
Symmetric Operators ◽  
Unbounded Linear Operators ◽  
Special Case

This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

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