scholarly journals Extremely Strong Boundary Points and Real-linear Isometries

2015 ◽  
Vol 38 (2) ◽  
pp. 477-490 ◽  
Author(s):  
Arya JAMSHIDI ◽  
Fereshteh SADY
Keyword(s):  
Boundary Points ◽  
Real Linear ◽  
Linear Isometries

scholarly journals Real-linear isometries between subspaces of continuous functions

2014 ◽  
Vol 413 (1) ◽  
pp. 229-241 ◽  
Author(s):  
Hironao Koshimizu ◽  
Takeshi Miura ◽  
Hiroyuki Takagi ◽  
Sin-Ei Takahasi
Keyword(s):  
Continuous Functions ◽  
Real Linear ◽  
Linear Isometries

2-Local real-linear isometries on C(1)([0, 1])

2021 ◽  
pp. 1-9
Author(s):  
Hironao Koshimizu ◽  
Takeshi Miura
Keyword(s):  
Real Linear ◽  
Linear Isometries

Real-linear isometries between certain subspaces of continuous functions

2013 ◽  
Vol 11 (11) ◽  
Author(s):  
Arya Jamshidi ◽  
Fereshteh Sady
Keyword(s):  
Metric Spaces ◽  
Continuous Functions ◽  
Supremum Norm ◽  
Hausdorff Spaces ◽  
Linear Isometry ◽  
Compact Metric Spaces ◽  
Separating Property ◽  
Similar Description ◽  
Real Linear ◽  
Linear Isometries

AbstractIn this paper we first consider a real-linear isometry T from a certain subspace A of C(X) (endowed with supremum norm) into C(Y) where X and Y are compact Hausdorff spaces and give a result concerning the description of T whenever A is a uniform algebra on X. The result is improved for the case where T(A) is, in addition, a complex subspace of C(Y). We also give a similar description for the case where A is a function space on X and the range of T is a real subspace of C(Y) satisfying a ceratin separating property. Next similar results are obtained for real-linear isometries between spaces of Lipschitz functions on compact metric spaces endowed with a certain complete norm.

WIGNER’S THEOREM IN -TYPE SPACES

2017 ◽  
Vol 97 (2) ◽  
pp. 279-284 ◽  
Author(s):  
WEIKE JIA ◽  
DONGNI TAN
Keyword(s):  
Functional Equation ◽  
Wigner’S Theorem ◽  
Type Spaces ◽  
Real Linear ◽  
Image Position ◽  
Formula Type ◽  
Wigner's Theorem ◽  
Linear Isometries

We investigate surjective solutions of the functional equation $$\begin{eqnarray}\displaystyle \{\Vert f(x)+f(y)\Vert ,\Vert f(x)-f(y)\Vert \}=\{\Vert x+y\Vert ,\Vert x-y\Vert \}\quad (x,y\in X), & & \displaystyle \nonumber\end{eqnarray}$$ where $f:X\rightarrow Y$ is a map between two real ${\mathcal{L}}^{\infty }(\unicode[STIX]{x1D6E4})$-type spaces. We show that all such solutions are phase equivalent to real linear isometries. This can be considered as an extension of Wigner’s theorem on symmetry for real ${\mathcal{L}}^{\infty }(\unicode[STIX]{x1D6E4})$-type spaces.

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