Self-induced compactness in Banach spaces

We consider the question: is every compact set in a Banach space X contained in the closed unit range of a compact (or even approximable) operator on X? We give large classes of spaces where the question has an affirmative answer, but observe that it has a negative answer, in general, for approximable operators. We further construct a Banach space failing the bounded compact approximation property, though all of its duals have the metric compact approximation propert

Optimal quantum tomography for states, measurements, and transformations

We present the first complete optimization of quantum tomography, for states, POVMs, and various classes of transformations, for arbitrary prior ensemble and arbitrary representation, giving corresponding feasible experimental schemes.Comment: 4 pages, 1 figur

On sequence spaces for Fr\'echet frames

We analyze the construction of a sequence space $\widetilde{\Theta}$, resp. a sequence of sequence spaces, in order to have $\{g_i\}$ as a $\widetilde{\Theta}$-frame or Banach frame for a Banach space $X$, resp. pre-$F$-frame or $F$-frame for a Fr\'echet space $X_F=\cap_{s\in {\mathbb N}_0} X_s$, where $\{X_s\}_{s\in {\mathbb N}_0}$ is a sequence of Banach spaces

A Study of the Pyrolysis Products of Kraft Lignin

In order to valorize lignin wastes to produce useful aromatic compounds, the thermal degradation pyrolysis of Kraft lignin in the absence of catalysts has been investigated at 350, 450, and 550 \ub0C. The high content of sulfur in the fresh sample led to the formation of S\u2010containing compounds in products whose evolution in the gas phase was monitored through GC\u2010MS analysis. Py-rolytic gas is rich in CH4, CO, CO2, and H2S with the presence of other sulfur compounds in smaller amounts (i.e., CH3SH, CH3\u2010S\u2010CH3, SO2, COS, and CS2). Biochar morphology and elemental composition have been investigated by means of SEM and EDX. The carbon content reaches ~90% after pyrolysis at 550 \ub0C, while the oxygen content showed a decreasing trend with increasing tempera-ture. From GC\u2010MS analysis, bio\u2010oil resulted rich in alkyl\u2010alkoxy phenols, together with (alkyl)dihy-droxy benzenes and minor amounts of hydrocarbons and sulfur compounds. NaOH/H2O and EtOH/H2O extraction were performed with the aim of extracting phenolic\u2010like compounds. Sodium hydroxide solution allowed a better but still incomplete extraction of phenolic compounds, leaving a bio\u2010oil richer in sulfur

Coefficient Quantization for Frames in Banach Spaces

Let $(e_i)$ be a fundamental system of a Banach space. We consider the problem of approximating linear combinations of elements of this system by linear combinations using quantized coefficients. We will concentrate on systems which are possibly redundant. Our model for this situation will be frames in Banach spaces.Comment: 33 page

Weighted complex projective 2-designs from bases: optimal state determination by orthogonal measurements

We introduce the problem of constructing weighted complex projective 2-designs from the union of a family of orthonormal bases. If the weight remains constant across elements of the same basis, then such designs can be interpreted as generalizations of complete sets of mutually unbiased bases, being equivalent whenever the design is composed of d+1 bases in dimension d. We show that, for the purpose of quantum state determination, these designs specify an optimal collection of orthogonal measurements. Using highly nonlinear functions on abelian groups, we construct explicit examples from d+2 orthonormal bases whenever d+1 is a prime power, covering dimensions d=6, 10, and 12, for example, where no complete sets of mutually unbiased bases have thus far been found.Comment: 28 pages, to appear in J. Math. Phy

Multipliers for p-Bessel sequences in Banach spaces

Multipliers have been recently introduced as operators for Bessel sequences and frames in Hilbert spaces. These operators are defined by a fixed multiplication pattern (the symbol) which is inserted between the analysis and synthesis operators. In this paper, we will generalize the concept of Bessel multipliers for p-Bessel and p-Riesz sequences in Banach spaces. It will be shown that bounded symbols lead to bounded operators. Symbols converging to zero induce compact operators. Furthermore, we will give sufficient conditions for multipliers to be nuclear operators. Finally, we will show the continuous dependency of the multipliers on their parameters.Comment: 17 page

Prime tight frames

We introduce a class of finite tight frames called prime tight frames and prove some of their elementary properties. In particular, we show that any finite tight frame can be written as a union of prime tight frames. We then characterize all prime harmonic tight frames and use this characterization to suggest effective analysis and synthesis computation strategies for such frames. Finally, we describe all prime frames constructed from the spectral tetris method, and, as a byproduct, we obtain a characterization of when the spectral tetris construction works for redundancies below two