Timeline for A universal operator between separable Banach spaces

7 events

when toggle format	what		by	license	comment
Jul 1, 2016 at 11:48	comment	added	Bill Johnson		It is worthwhile mentioning that these examples use the existence of many spaces that fail the bounded approximation property. They are needed because of the Kadec-Pelczynski example of a Banach space $X$ with a Schauder basis such that every separable Banach space with the bounded approximation property is isomorphic to a complemented subspace of $X$.
Jun 30, 2016 at 19:42	history	edited	Kevin Beanland	CC BY-SA 3.0	added 2 characters in body
Jun 30, 2016 at 19:32	comment	added	Kevin Beanland		The problem would have seemed much better if I hadn't listed the Johnson-Szankowski papers. It took me longer to write than it should have taken me to come up with Bill's example once I found the J-S results.
Jun 30, 2016 at 19:29	history	edited	Kevin Beanland	CC BY-SA 3.0	added 2 characters in body
Jun 30, 2016 at 18:20	comment	added	Kevin Beanland		Bill: Thanks, should have seen that!
Jun 30, 2016 at 18:11	comment	added	Bill Johnson		If the identity operator on $E$ factors through $U:X\to Y$ via $(A,B)$, then $A$ is an isomorphic embedding and $BAU$ is a projection from $X$ onto $AE$, so you know answer to (1). Similarly, the answer to (2) is also negative because of JFA 2009.
Jun 30, 2016 at 17:51	history	asked	Kevin Beanland	CC BY-SA 3.0