On weak and strong Peano theorems

We say that the Peano theorem holds for a topological vector space $E$ if, for any continuous mapping $f : {\Bbb R}\times E \to E$ and any $(t(0), x(0))$ is an element of ${\Bbb R}\times E$, the Cauchy problem $\dot x(t) = f(t,x(t))$, $x(t(0)) = x(0)$, has a solution in some neighborhood of $t(0)$. We say that the weak version of Peano theorem holds for $E$ if, for any continuous map $f : {\Bbb R}\times E \to E$, the equation $\dot x(t) = f (t, x(t))$ has a solution on some interval. We construct an example (answering a question posed by S. G. Lobanov) of a Hausdorff locally convex topological vector space E for which the weak version of Peano theorem holds and the Peano theorem fails to hold. We also construct a Hausdorff locally convex topological vector space E for which the Peano theorem holds and any barrel in E is neither compact nor sequentially compact.

Time operators for one parameter semigroups

We develop two simple approaches to the construction of time operators for semigroups of continuous linear operators in Hilbert spaces provided that the generators of these semigroups are normal operators. The first approach enables us to give explicit formulas (in the spectral representations) both for the time operators and for their eigenfunctions. The other approach provides no explicit formula. However, it enables us to find necessary and sufficient conditions for the existence of time operators for semigroups of continuous linear operators in separable Hilbert spaces with normal generators. Time superoperators corresponding to unitary groups are also discussed.

On linear extension operators

We construct a countable-dimensional Hausdorff locally convex topological vector space $E$ and a stratifiable closed linear subspace $F$ subset of $E$ such that any linear extension operator from $C_b(F)$ to $C_b(E)$ is unbounded (here $C_b(X)$ stands for the Banach space of continuous bounded real-valued functions on $X$).

Three constructive examples of separable pre-Hilbert spaces nonisomorphic to their closed hyperplanes

An example of a sigma -compact infinite-dimensional pre-Hilbert space H is constructed such that any continuous linear operator T: H --> H is of the form T = lambdaI + F for some lambda is an element of R and for a finite-dimensional continuous linear operator F. A class of simple examples of pre-Hilbert spaces nonisomorphic to their closed hyperplanes is given. A sigma -compact pre-Hilbert space H isomorphic to H x R x R and nonisomorphic to H x R is also constructed.

Integral completeness of locally convex spaces

A locally convex space X is said to be integrally complete if each continuous mapping f: [0, 1] --> X is Riemann integrable. A criterion for integral completeness is established. Readily verifiable sufficient conditions of integral completeness are proved.

On stratifiable locally convex spaces

In the present paper we prove several results on the stratifiability of locally convex spaces. In particular, we show that a free locally convex sum of an arbitrary set of stratifiable LCS is a stratifiable LCS, and that all locally convex F'-spaces whose bounded subsets are metrizable are stratifiable. Moreover, we prove that a strict inductive limit of metrizable LCS is stratifiable and establish the stratifiability of many important general and specific spaces used in functional analysis. We also construct some examples that clarify the relationship between the stratifiability and other properties.

"Bobok" y "Pedro Páramo", dos narraciones sobre muertos

El presente estudio realiza un análisis comparativo entre la novela del mexicano Juan Rulfo, Pedro Páramo (1955), y un cuento del escritor ruso Dostoievski que trata también el tema del Más allá, titulado Bobok (1873). Paralelamente, se trabaja con la posibilidad de que el relato ruso hubiese podido ser una más de las fuentes literarias de la novela mexicana, y se trata de determinar las posibles conexiones -directas o indirectas- entre las dos obras. Ambas son puestas en común por su género literario, y a partir de ahí se estudian los elementos constitutivos que tienen en común, sus afinidades y divergencias más llamativas.

“Hegemony Protected by the Armour of Coercion”: Dashiell Hammett’s Red Harvest and the State

This article argues that Dashiell Hammett's 1929 novel Red Harvest is best understood in the context of the consolidation and expansion of the US state following the First World War and the Russian Revolution. It also argues that Hammett's novel constitutes a highly significant articulation of theoretical debates about the nature of political authority and state power in the modern era and speaks about the transition of one state formation to another. Insofar as Red Harvest explores the way in which the state's coercive and ethical character are bound up together, this article argues that Hammett's novel draws upon an understanding of political authority and state power primarily derived from Gramsci, via Marx. Gramsci insists that control cannot be maintained through force alone (and his conception of hegemony, in turn, suggests a power bloc that can become fragmented and disunited in a war of position). In the same way, Red Harvest traces the transformation of the “economic-corporate” state into the expanded or “ethical” State but crucially any ethical dimension, as Gramsci notes, is always beholden to the needs of the capitalist economy. As such, the apparently arbitrary bloodshed in the novel is conceived as a relatively minor realignment in the ranks of the capitalist classes – certainly less serious than the miners' strike that prefigures the novel. What makes this realignment significant is that it calls attention to the state both as repressive and as a site of conflict and compromise. Here, the work performed by the Continental Op and by the crime novel in general – simultaneously buttressing and, to some extent, contesting the power of the state – needs to be understood as part of the process by which the state is consistently enacting hegemony (albeit protected by the armour of coercion). The article concludes by pointing out that while Gramsci is perhaps too willing to dwell upon the state's expanded reach, Red Harvest is more interested in examining possible “cracks and fissures” in the state formation, even if the critique it ultimately offers goes nowhere and yields nothing.