Property (ω) and quasi-class (A, k) operators
In this paper, we prove the following assertions: (i) If T is of quasi-class (A, k), then T is polaroid and reguloid; (ii) If T or T* is an algebraically of quasi-class (A, k) operator, then Weyls theorem holds for f(T) for every f ∈ Hol(σ(T)); (iii) If T* is an algebraically of quasi-class (A, k) operator, then a-Weyls theorem holds for f(T) for every f ∈ Hol(σ(T)); (iv) If T* is algebraically of quasi-class (A, k) then property (ω) holds for T.
Fredholm and Local Spectral Theory, with Applications to Multipliers
Preface 1. The Kato decomposition property 1. Hyper-kernel and hyper-range of an operator 2. Semi-regular operators on Banach spaces 3. Analytical core of an operator 4. The semi-regular spectrum of an operator 5. The generalized Kato decomposition 6. Semi-Fredholm operators 7. Quasi-nilpotent part of an operator 2. The single-valued extension property 1. Local spectrum and SVEP 2. The SVEP at a point 3. A local spectral mapping theorem 4. Algebraic spectral subspaces 5. Weighted shift operators and SVEP 3. The SVEP and Fredholm theory 1. Ascent, descent, and the SVEP 2. The SVEP for operators of Kato type 3. The SVEP on the components of rho kappa (T) 4. The Fredholm, Weyl, and Browder spectra 5. Compressions 6. Some spectral mapping theorems 7. Isolated points of the spectrum 8. Weyl's theorem 9. Riesz operators 10. The spectra of some operators 4. Multipliers of commutative Banach algebras 1. Definitions and elementary properties 2. The Helgason-Wang function 3. The first spectral properties of multipliers 4. Multipliers of group algebras 5. Multipliers of Banach algebras with orthogonal basis 6. Multipliers of commutative H* algebras 5. Abstract Fredholm theory 1. Inessential ideals 2. The socle 3. The socle of semi-prime Banach algebras 4. Riesz algebras 5. Fredholm elements of Banach algebras 6. Compact multipliers 7. Weyl multipliers 8. Multipliers of Tauberian regular commutative algebras 9. Some concrete cases 10. Browder spectrum of a multiplier 6. Decomposability 1. Spectral maximal subspaces 2. Decomposable operators on Banach spaces 3. Super-decomposable operators 4. Decomposable right shift operators 5. Decomposable multipliers 6. Riesz multipliers 7. Decomposable convolution operators 7.Perturbation classes of operators 1. Inessential operators between Banach spaces 2. Omega+ and Omega- operators 3. Strictly singular and strictly cosingular operators 4. Improjective operators 5. Incomparability between Banach spaces Bibliography Index
The risk of being sued by those damaged by regulatory or enforcement action: over‐regulation of financial services?
Discusses the impact of regulatory and enforcement action on banking and financial services, focusing on Switzerland, which is one of the most developed financial centres. Describes the recent increase in legislation which introduces corporate criminal liability, plus the far‐reaching Money Laundering Ordinance with its stronger due diligence requirements. Points out that in the field of financial services, liberalisation and globalisation have been met with more rather than less regulation. Concludes that, while greater regulation can be viewed as a reasonable price to pay for globalised financial services, the over‐regulation of Swiss financial services needs to be rationalised.