Isomorphic embedding of ℓ p n , 1

2001 ◽  
Vol 122 (1) ◽  
pp. 371-380 ◽  
Author(s):  
Assaf Naor ◽  
Artem Zvavitch
Keyword(s):  
Isomorphic Embedding

scholarly journals Fixed-point-free embeddings of graphs in their complements

1978 ◽  
Vol 1 (3) ◽  
pp. 335-338 ◽  
Author(s):  
Seymour Schuster
Keyword(s):  
Fixed Point ◽  
Isomorphic Embedding

The following is proved: IfGis a labeled(p,p−2)graph wherep≥2, then there exists an isomorphic embeddingϕofGin its complementG¯such thatϕhas no fixed vertices. The extension to(p,p−1)graphs is also considered.

scholarly journals THE QUOTIENT ALGEBRA OF COMPACT-BY-APPROXIMABLE OPERATORS ON BANACH SPACES FAILING THE APPROXIMATION PROPERTY

2019 ◽  
pp. 1-23
Author(s):  
HANS-OLAV TYLLI ◽  
HENRIK WIRZENIUS
Keyword(s):  
Banach Spaces ◽  
Structural Properties ◽  
Approximation Property ◽  
Quotient Algebra ◽  
Isomorphic Embedding ◽  
Compact Approximation

We initiate a study of structural properties of the quotient algebra ${\mathcal{K}}(X)/{\mathcal{A}}(X)$ of the compact-by-approximable operators on Banach spaces $X$ failing the approximation property. Our main results and examples include the following: (i) there is a linear isomorphic embedding from $c_{0}$ into ${\mathcal{K}}(Z)/{\mathcal{A}}(Z)$ , where $Z$ belongs to the class of Banach spaces constructed by Willis that have the metric compact approximation property but fail the approximation property, (ii) there is a linear isomorphic embedding from a nonseparable space $c_{0}(\unicode[STIX]{x1D6E4})$ into ${\mathcal{K}}(Z_{FJ})/{\mathcal{A}}(Z_{FJ})$ , where $Z_{FJ}$ is a universal compact factorisation space arising from the work of Johnson and Figiel.

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