The unique decomposition property and the Banach-Stone theorem

Author(s):  
Audrey Curnock ◽  
John Howroyd ◽  
Ngai-Ching Wong
2017 ◽  
Vol 60 (1) ◽  
pp. 35-50
Author(s):  
MUNEO CHŌ ◽  
EUNGIL KO ◽  
JI EUN LEE

AbstractIn this paper, we study spectral properties and local spectral properties of ∞-complex symmetric operators T. In particular, we prove that if T is an ∞-complex symmetric operator, then T has the decomposition property (δ) if and only if T is decomposable. Moreover, we show that if T and S are ∞-complex symmetric operators, then so is T ⊗ S.


2022 ◽  
Vol 14 (2) ◽  
pp. 370
Author(s):  
Cameron Proctor ◽  
Cedelle Pereira ◽  
Tian Jin ◽  
Gloria Lim ◽  
Yuhong He

Efforts to monitor terrestrial decomposition dynamics at broad spatial scales are hampered by the lack of a cost-effective and scalable means to track the decomposition process. Recent advances in remote sensing have enabled the simulation of litter spectra throughout decomposition for grasses in general, yet unique decomposition pathways are hypothesized to create subtly different litter spectral signatures with unique ecosystem functional significance. The objectives of this study were to improve spectra–decomposition linkages and thereby enable the more comprehensive monitoring of ecosystem processes such as nutrient and carbon cycles. Using close-range hyperspectral imaging, litter spectra and multiple decomposition metrics were concurrently monitored in four classes of naturally decayed litter under four decomposition treatments. The first principal component accounted for approximately 94% of spectral variation in the close-range imagery and was attributed to the progression of decomposition. Decomposition-induced spectral changes were moderately correlated with the leaf carbon to nitrogen ratio (R2 = 0.52) and sodium hydroxide extractables (R2 = 0.45) but had no correlation with carbon dioxide flux. Temperature and humidity strongly influenced the decomposition process but did not influence spectral variability or the patterns of surface decomposition. The outcome of the study is that litter spectra are linked to important metrics of decomposition and thus remote sensing could be utilized to assess decomposition dynamics and the implications for nutrient recycling at broad spatial scales. A secondary study outcome is the need to resolve methodological challenges related to inducing unique decomposition pathways in a lab environment. Improving decomposition treatments that mimic real-world conditions of temperature, humidity, insolation, and the decomposer community will enable an improved understanding of the impacts of climatic change, which are expected to strongly affect microbially mediated decomposition.


2010 ◽  
Vol 106 (1) ◽  
pp. 88 ◽  
Author(s):  
Luis A. Dupont ◽  
Rafael H. Villarreal

The normality of a monomial ideal is expressed in terms of lattice points of blocking polyhedra and the integer decomposition property. For edge ideals of clutters this property characterizes normality. Let $G$ be the comparability graph of a finite poset. If $\mathrm{cl}(G)$ is the clutter of maximal cliques of $G$, we prove that $\mathrm{cl}(G)$ satisfies the max-flow min-cut property and that its edge ideal is normally torsion free. Then we prove that edge ideals of complete admissible uniform clutters are normally torsion free.


2006 ◽  
Vol 80 (3) ◽  
pp. 359-366 ◽  
Author(s):  
Dinh Van Huynh ◽  
S. Tariq Rizvi

AbstractA module M is said to satisfy the condition (℘*) if M is a direct sum of a projective module and a quasi-continuous module. In an earlier paper, we described the structure of rings over which every (countably generated) right module satisfies (℘*), and it was shown that such a ring is right artinian. In this note some additional properties of these rings are obtained. Among other results, we show that a ring over which all right modules satisfy (℘*) is also left artinian, but the property (℘*) is not left-right symmetric.


Sign in / Sign up

Export Citation Format

Share Document