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The Cesaro operator $\mathsf{C}$, when acting in the classical growth Banach spaces $A^{-\gamma}$ and $A_0^{-\gamma}$, for $\gamma > 0 $, of analytic functions on $\mathbb{D}$, is investigated. Based on a detailed knowledge of their spectra (due to A. Aleman and A.-M. Persson) we are able to determine the norms of these operators precisely. It is then possible to characterize the mean ergodic and related properties of $\mathsf{C}$ acting in these spaces. In addition, we determine the largest Banach space of analytic functions on $\mathbb{D}$ which $\mathsf{C}$ maps into $A^{-\gamma}$ (resp. into $A_0^{-\gamma}$); this optimal domain space always contains $A^{-\gamma}$ (resp. $A_0^{-\gamma}$) as a proper subspace.

We study weighted $H^\infty$ spaces of analytic functions on the open unit disc in the case of non-doubling weights, which decrease rapidly with respect to the boundary distance. We characterize the solid hulls of such spaces and give quite explicit representations of them in the case of the most natural exponentially decreasing weights.

We study weighted $H^\infty$ spaces of analytic functions on the open unit disc in the case of non-doubling weights, which decrease rapidly with respect to the boundary distance. We characterize the solid hulls of such spaces and give quite explicit representations of them in the case of the most natural exponentially decreasing weights.

Let $X$ be a separable Banach space with a separating polynomial. We show that there exists $C\geq 1$ (depending only on $X$) such that for every Lipschitz function $f:X\rightarrow\mathbb{R}$, and every $\epsilon>0$, there exists a Lipschitz, real analytic function $g:X\rightarrow\mathbb{R}$ such that $|f(x)-g(x)|\leq \epsilon$ and $\textrm{Lip}(g)\leq C\textrm{Lip}(f)$. This result is new even in the case when $X$ is a Hilbert space. Furthermore, in the Hilbertian case we also show that $C$ can be assumed to be any number greater than 1.

Let X be a separable Banach space which admits a separating polynomial; in particular X a separable Hilbert space. Let $f:X \rightarrow R$ be bounded, Lipschitz, and $C^1$ with uniformly continuous derivative. Then for each {\epsilon}>0, there exists an analytic function $g:X \rightarrow R$ with $|g-f|

This "how-to" book covers everything for the 1800's illusionist, from stage presence & dress, program and stage arrangement, to how to do tricks with cards, coins, watches, rings, handkerchiefs, dominoes and dice, cups and balls, hats, and other apparatus. "I have purposely limited my disclosures to such illusions as have been sufficiently long before the public to be fairly regarded as common property. Within this limit I have endeavored to make my explanations as complete as possible; but to go beyond it would be to infringe a moral copyright, and to deprive gentlemen to whom Modern Magic is especially indebted, of the well-earned fruits of their labor and invention." - Summary by TriciaG<br><br>Proof-Listeners: Joyful in MN, Billl Boerst

2From Makin to Bougainville: Marine Raiders in the Pacific War

By Jon T. Hoffman

In February 1942, Lieutenant General Thomas Holcomb, the Commandant of the Marine Corps, ordered the creation of a new unit designated the 1st Marine Raider Battalion. This elite force, and its three sister battalions, went on to gain considerable fame for fighting prowess in World War II. There is more to the story of these units, however, than a simple tale of combat heroics. The inception, growth, and sudden end of the raiders reveals a great deal about the development and conduct of amphibious operations during the war, and about the challenges the Corps faced in expanding from 19,000 men to nearly a half million. The raiders also attracted more than their share of strong leaders. The resulting combination of courage, doctrine, organization, and personalities makes this one of the most interesting chapters in Marine Corps history. - Summary by Jon T. Hoffman