Composition Operators and Endomorphisms

If $b$ is an inner function, then composition with $b$ induces an endomorphism, $\beta$, of $L^\infty(\mathbb{T})$ that leaves $H^\infty(\mathbb{T})$ invariant. We investigate the structure of the endomorphisms of $B(L^2(\mathbb{T}))$ and $B(H^2(\mathbb{T}))$ that implement $\beta$ through the representations of $L^\infty(\mathbb{T})$ and $H^\infty(\mathbb{T})$ in terms of multiplication operators on $L^2(\mathbb{T})$ and $H^2(\mathbb{T})$. Our analysis, which is based on work of R. Rochberg and J. McDonald, will wind its way through the theory of composition operators on spaces of analytic functions to recent work on Cuntz families of isometries and Hilbert $C^*$-modules

More than just a bracelet: the use of material symbolism to communicate love

There is growing recognition of the place of love in residential care for children (Smith, 2009). This paper is a critical analysis of a range of existing research on residential child care as well as studies of material culture and of care relationships more broadly. It argues that, despite increasing regulation and surveillance, adults and children find ways to show and feel love in the context of residential care. Whilst love may be regarded as something to be avoided or indeed prohibited in an adult/child care setting these deep bonds find expression in the everyday life of the children's home. By looking at love in this embodied way, the 'realness' of material things to assert connection and recognition of love (Layne, 2000) is examined. As Gorenstein (1996, p.8) suggests 'objects...[are] the perfect vehicles for conveying themes that are not commonly accepted in a community'. The paper emphasises the recognition of these symbolic and metaphorical forms of communication in practice