We introduce a technique that is helpful in evaluating the reflexivity index of several classes of topological spaces and lattices. The main results are related to products: we give a sufficient condition for the product of a topological space and a nest of balls to have low reflexivity index and determine the reflexivity index of all compact connected 2-manifolds.

Right-Node Raising is generally considered to impose stricter identity conditions than other kinds of ellipsis, such as VP ellipsis, according to Hankamer & Sag 1976 and Hardt 1993. In this paper, we investigate voice mismatch in French Right-Node Raising (RNR) through a corpus study and two experiments. We show that RNR with voice mismatch can be found in a written corpus (frTenTen 2012) and that many examples involve coordination of a reflexive active and a short passive form. We suggest this is because semantic contrast (here, between self and external agent) plays a role according to Hartmann (2000) and Abeillé and Mouret (2010). We ran two acceptability judgement experiments to test voice mismatch and semantic contrast. We did not find any penalty for voice mismatch with VP ellipsis but an interaction with semantic contrast. We also found an effect of semantic contrast when coordinating an active and a passive VP without participle ellipsis. We conclude that voice mismatch is acceptable with RNR and propose a Head-driven Phrase-Structure Grammar (HPSG) analysis, following Chaves (2014) and Shiraïshi et al. (2019).

The paper focuses on the syntax and semantics of the French verbal prefix auto. It is proposed that auto is an intensifier stating that no agent other than the one specified in the clause (agent-focusing), or, in anticausative clauses, no agent (agent-denying), is responsible for the event. Syntactically, auto merges with a verbal projection, and the nature of the constituent to which it attaches determines and constrains the interpretation of the clause. The proposed analysis of auto provides support for generative approaches in which a v head introduces the external argument role, while a grammatical Voice head determines its syntactic realization.

This paper argues that inalienable relational nouns in Mandarin Chinese, specifically kinship nouns (KNs, e.g. father, sister) and body-part nouns (BPNs, e.g. head, face), have an implicit reflexive argument. Based on a syntactic comparison between KNs, BPNs, locally and long-distance bound reflexives, we argue that the implicit reflexive arguments of BPNs must be locally bound, whereas that of KNs can either be locally or long-distance bound. We conclude that these two types of implicit arguments in Mandarin Chinese correspond to locally and long-distance bound reflexives, respectively. We analyze this difference in connection with binding theory and a theory of logophoricity. We argue that the implicit argument of BPNs is a locally bound anaphor and cannot be used as a logophor, whereas that of KNs can, supporting a proposal that the logophoric property leads to long-distance binding, as argued by Huang & Liu’s (2001) for reflexives in Mandarin Chinese.

This paper presents an analysis of reflexives in Shona. Taking seriously the observation that the reflexive morpheme zvi- is homophonous with one of Shona's object markers, I argue that this homophony is not accidental. Rather, the morpheme that emerges in reflexive contexts is object marking triggered by a covert anaphor. The analysis rests on two planks: first, establishing that zvi- is the default agreement form in the language generally; and second, establishing that a covert anaphor may trigger such an agreement. In so doing, a treatment of object marking as the exponence of discourse-givenness is advanced. The analysis is compatible with treatments of object marking in Shona as either an agreement affix or a clitic. Theoretical issues related to default agreement, covert anaphors, and distinctions between discourse-givenness and topicality are also discussed, along with an alternative account treating zvi- as a valence-reducing derivational affix.

A definition of the reflexive index of a family of (closed) subspaces of a complex, separable Hilbert space $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}H$ is given, analogous to one given by D. Zhao for a family of subsets of a set. Following some observations, some examples are given, including: (a) a subspace lattice on $H$ with precisely five nontrivial elements with infinite reflexive index; (b) a reflexive subspace lattice on $H$ with infinite reflexive index; (c) for each positive integer $n$ satisfying dim $H\ge n+1$, a reflexive subspace lattice on $H$ with reflexive index $n$. If $H$ is infinite-dimensional and ${\mathcal{B}}$ is an atomic Boolean algebra subspace lattice on $H$ with $n$ equidimensional atoms and with the property that the vector sum $K+L$ is closed, for every $K,L\in {\mathcal{B}}$, then ${\mathcal{B}}$ has reflexive index at most $n$.

We study the reflexivity and transitivity of a double triangle lattice of subspaces in a Hilbert space. We show that the double triangle lattice is neither reflexive nor transitive when some invertibility condition is satisfied (by the restriction of a projection under another). In this case, we show that the reflexive lattice determined by the double triangle lattice contains infinitely many projections, which partially answers a problem of Halmos on small lattices of subspaces in Hilbert spaces.

In this paper, we give a new characterization of reflexive Banach spaces in terms of the sum of two closed bounded convex sets.

A Toeplitz decomposition of a locally convez space E into subspaces (Ek) with continuous projections (Pk) is a decomposition of every x ∈ E as x = ΣkPkx where ordinary summability has been replaced by summability with respect to an infinite and row-finite matrix. We extend to the setting of Toeplitz decompositions a number of results about the locally convex structure of a space with a Schauder decomposition. Namely, we give some necessary or sufficient conditions for being reflexive, a Montel space or a Schwartz space. Roughly speaking, each of these locally convex properties is linked to a property of the convergence of the decomposition. We apply these results to study some structural questions in projective tensor products and spaces with Cesàro bases.

The geometric notions of a gap and gap points between “concentric” spheres in a normed linear space are introduced and studied. The existence of gap points characterizes finitedimensional spaces. General conditions are given under which an infinite-dimensional normed linear space admits concentric spheres such that both these spheres and their dual spheres fail to have gap points.