ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.1.1

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.1.17

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.1.32

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.1.55

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.1.62

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

This paper discusses the eigenvalue problem associated with the weighted Sturm‐Liouville differential equation given, for με(−1,1), by(I)−{(1−μ2)(s/τ)+1(μ2−τ2)Y′(μ)}′−s2τ2(1−μ2)(s/τ)−1Y(μ)=λ(1−μ2)(s/τ)Y(μ)where s and τ are parameters, withsa non‐zero integer, and 0<τ<1; λ ε C determines the eigenvalues. This problem can be derived from the original form of the Laplace tidal wave equation(II)−{1−μ2μ2−τ2y′(μ)}′+{1μ2−τ2{sτ[μ2+τ2μ2−τ2]+s21−μ2}}y(μ)=λy(μ)salso valid for με(−1,1), on using quasi‐derivatives and transformation theory.The important feature of interest in (I) and (II) is that the leading coefficient (1 − μ2)(s/τ)+1/(μ2−τ2) in (I) (or (1 − μ2)/(μ2−τ2) in (II)) changes sign over the interval (−1,1) which leads to interesting spectral properties of the associated differential operator; in particular it is shown that the spectrum of this operator is unbounded aboveandbelow, and is discrete and simple. Additionally the eigenfunctions of the unique operator generated by (I) are shown to be complete in the weighted Hilbert function space L2w(−1,1) whereW(μ) = (1 − μ2)s/τ(με{− 1,1)). This result implies the completeness, inL2(−1,1), of the eigenfunctions (commonly called the Hough functions) of the unitarily equivalent operator generated by equation (II).

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.1.79

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.1.97

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

We investigate the role played by semigroups in the study of weakly compact homomorphisms between certain Banach algebras.

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.1.113

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

The weak∗‐Haagerup tensor productM⊗w∗hNof two von Neumann algebras is related to the Haagerup tensor productM⊗hNin the same way that the von Neumann algebra tensor product is related to the spatial tensor product. Many of the fundamental theorems about completely bounded multilinear maps may be deduced from elementary properties of the weak∗‐Haagerup tensor product. We show thatX∗⊗w∗hY∗=(X⊗hY)∗for all operator spacesXandY. The weak∗‐Haagerup tensor product has simple characterizations and behaviour with reference to slice map properties. The tensor product of two (not necessarily self‐adjoint) operator algebras is proven to have many strong commutant properties. All operator spaces possess a certain approximation property which is related to this tensor product. The connection between bimodule maps and commutants is explored.

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.1.126

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.1.145

出版商:Oxford University Press    

年代:2016

数据来源: WILEY