scholarly journals On Expansive Mappings

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1004
Author(s):  
Marat V. Markin ◽  
Edward S. Sichel
Keyword(s):  
Metric Spaces ◽  
Original Proof ◽  
Compact Metric Spaces ◽  
Total Boundedness

When finding an original proof to a known result describing expansive mappings on compact metric spaces as surjective isometries, we reveal that relaxing the condition of compactness to total boundedness preserves the isometry property and nearly that of surjectivity. While a counterexample is found showing that the converse to the above descriptions do not hold, we are able to characterize boundedness in terms of specific expansions we call anticontractions.

scholarly journals A new proof of the Banach-stone theorem

1998 ◽  
Vol 57 (1) ◽  
pp. 55-58
Author(s):  
N.J. Cutland ◽  
G.B. Zimmer
Keyword(s):  
Metric Spaces ◽  
Continuous Functions ◽  
Hausdorff Spaces ◽  
Original Proof ◽  
Compact Metric Spaces ◽  
Peak Point ◽  
Standard Part ◽  
Peak Functions ◽  
Stone Theorem

Banach's original proof of the Banach-Stone theorem for compact metric spaces uses peak functions, that is, continuous functions which assume their norm in just one point. We show by using nonstandard methods that the peak point approach also works for compact Hausdorff spaces. The peak functions are replaced by internal functions whose standard part is supported in one monad.

scholarly journals The Blum-Hanson Property

2019 ◽  
Vol 6 (1) ◽  
pp. 92-105
Author(s):  
Sophie Grivaux
Keyword(s):  
Banach Space ◽  
Hilbert Spaces ◽  
Separable Banach Space ◽  
Metric Spaces ◽  
Compact Metric Spaces ◽  
Theoretic Motivation

AbstractGiven a (real or complex, separable) Banach space, and a contraction T on X, we say that T has the Blum-Hanson property if whenever x, y ∈ X are such that Tnx tends weakly to y in X as n tends to infinity, the means{1 \over N}\sum\limits_{k = 1}^N {{T^{{n_k}}}x} tend to y in norm for every strictly increasing sequence (nk) k≥1 of integers. The space X itself has the Blum-Hanson property if every contraction on X has the Blum-Hanson property. We explain the ergodic-theoretic motivation for the Blum-Hanson property, prove that Hilbert spaces have the Blum-Hanson property, and then present a recent criterion of a geometric flavor, due to Lefèvre-Matheron-Primot, which allows to retrieve essentially all the known examples of spaces with the Blum-Hanson property. Lastly, following Lefèvre-Matheron, we characterize the compact metric spaces K such that the space C(K) has the Blum-Hanson property.

scholarly journals The box product of countably many compact metric spaces

1972 ◽  
Vol 2 (4) ◽  
pp. 293-298 ◽  
Author(s):  
Mary Ellen Rudin
Keyword(s):  
Metric Spaces ◽  
Compact Metric Spaces ◽  
Box Product

Common fixed points for self mappings on compact metric spaces

2013 ◽  
Vol 219 (12) ◽  
pp. 6804-6808 ◽  
Author(s):  
Cristina Di Bari ◽  
Pasquale Vetro
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Compact Metric Spaces

DIAGONALIZATION MODULO NORM IDEALS AND HAUSDORFF DIMENSIONALITY

2000 ◽  
Vol 11 (08) ◽  
pp. 1057-1078
Author(s):  
JINGBO XIA
Keyword(s):  
Hausdorff Measure ◽  
Metric Spaces ◽  
Adjoint Operator ◽  
Trace Class ◽  
Multiplication Operators ◽  
Von Neumann ◽  
Dimensional Hausdorff Measure ◽  
One Dimensional ◽  
Compact Metric Spaces ◽  
The One

Kuroda's version of the Weyl-von Neumann theorem asserts that, given any norm ideal [Formula: see text] not contained in the trace class [Formula: see text], every self-adjoint operator A admits the decomposition A=D+K, where D is a self-adjoint diagonal operator and [Formula: see text]. We extend this theorem to the setting of multiplication operators on compact metric spaces (X, d). We show that if μ is a regular Borel measure on X which has a σ-finite one-dimensional Hausdorff measure, then the family {Mf:f∈ Lip (X)} of multiplication operators on T2(X, μ) can be simultaneously diagonalized modulo any [Formula: see text]. Because the condition [Formula: see text] in general cannot be dropped (Kato-Rosenblum theorem), this establishes a special relation between [Formula: see text] and the one-dimensional Hausdorff measure. The main result of the paper is that such a relation breaks down in Hausdorff dimensions p>1.

scholarly journals Classification Of Locally 2-Connected Compact Metric Spaces

COMBINATORICA ◽  
2004 ◽  
Vol 25 (1) ◽  
pp. 85-103 ◽  
Author(s):  
Carsten Thomassen
Keyword(s):  
Metric Spaces ◽  
Compact Metric Spaces

scholarly journals AVERAGE SHADOWING PROPERTIES ON COMPACT METRIC SPACES

2006 ◽  
Vol 21 (2) ◽  
pp. 355-361 ◽  
Author(s):  
Jong-Jin Park ◽  
Yong Zhang
Keyword(s):  
Metric Spaces ◽  
Compact Metric Spaces

scholarly journals STOPPED DECISION PROCESS ON COMPACT METRIC SPACES

10.5109/13044 ◽  
1970 ◽  
Vol 14 (1/2) ◽  
pp. 51-60
Author(s):  
Seiichi Iwamoto
Keyword(s):  
Decision Process ◽  
Metric Spaces ◽  
Compact Metric Spaces

scholarly journals Stationary points for set-valued mappings on two metric spaces

2001 ◽  
Vol 28 (7) ◽  
pp. 427-432
Author(s):  
Zeqing Liu ◽  
Qingtao Liu ◽  
Shin Min Kang
Keyword(s):  
Stationary Point ◽  
Metric Spaces ◽  
Stationary Points ◽  
Compact Metric Spaces ◽  
Set Valued Mappings

We give stationary point theorems of set-valued mappings in complete and compact metric spaces. The results in this note generalize a few results due to Fisher.

Learning Over Compact Metric Spaces

2004 ◽  
pp. 239-254 ◽  
Author(s):  
H. Quang Minh ◽  
Thomas Hofmann
Keyword(s):  
Metric Spaces ◽  
Compact Metric Spaces
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