Infinitesimal analysis of l ∞ in its mackey topology

1983 ◽  
pp. 204-213
Author(s):  
K. D. Stroyan
Keyword(s):  
Mackey Topology ◽  
Infinitesimal Analysis

scholarly journals QUASI - MACKEY TOPOLOGY

2007 ◽  
Vol 26 (3) ◽  
Author(s):  
SURJIT SINGH KHURANA
Keyword(s):  
Mackey Topology

AN INFINITESIMAL ANALYSIS OF THE STOP-LOSS-START-GAIN STRATEGY

2005 ◽  
Vol 08 (05) ◽  
pp. 623-633 ◽  
Author(s):  
SIU-AH NG
Keyword(s):  
Trading Strategy ◽  
Elementary Derivation ◽  
Riemann Sum ◽  
Black Scholes ◽  
Infinitesimal Analysis ◽  
Stop Loss

The paradox of the Stop-Loss-Start-Gain trading strategy is resolved by showing that along the hyperfinite timeline the strategy incurs infinitesimal losses summing up to a non-infinitesimal amount. As a consequence, the Black–Scholes formula is derived using only hyperreal arithmetic and Riemann sum, probably the most elementary derivation thus far.

Naive Foundations of Infinitesimal Analysis

2002 ◽  
pp. 10-34
Author(s):  
E. I. Gordon ◽  
A. G. Kusraev ◽  
S. S. Kutateladze
Keyword(s):  
Infinitesimal Analysis

Mackey duals and almost shrinking bases

1973 ◽  
Vol 74 (1) ◽  
pp. 73-81 ◽  
Author(s):  
N. J. Kalton
Keyword(s):  
Banach Space ◽  
Weak Topology ◽  
Norm Topology ◽  
Weak Basis ◽  
Mackey Topology ◽  
Dual Sequence

Suppose (en) is a basis of a Banach space E, and that (e′n) is the dual sequence in E′. Then if (e′n) is a basis of E′ in the norm topology (i.e. (en) is shrinking) it follows that E′ is norm separable: it is easy to give examples of spaces E for which this is not so. Therefore there are plenty of spaces which cannot have a shrinking basis. This leads one to consider whether it might not be reasonable to replace the norm topology on E′ by one which is always separable (provided E is separable). Of course, the weak*-topology σ(E′, E) is one possibility (Köthe (17), p. 259); then it is trivial that (e′n) is a weak*-basis of E′. However, if the weak*-topology is separable, then so is the Mackey topology τ(E′, E) on E′, and so we may ask whether (e′n) is a basis of (E′,τ(E′, E)).

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