2,223 reputation
624
bio website maths.lancs.ac.uk/~kania
location Lancaster, United Kingdom
age
visits member for 4 years
seen 8 hours ago

May
15
awarded  Yearling
May
8
awarded  Popular Question
May
5
revised B(H) as a direct sum of a closed two sided ideal and a subalgebra
added 285 characters in body
May
5
comment constant rank theorem for banach spaces
Yes, I meant Schauder basis too.
May
5
comment constant rank theorem for banach spaces
@Jochen Wengenroth, a separable Banach space need not have a basis so strictly speaking these two things are not equivalent :-)
May
1
revised Predual of a Direct Sum of Banach Spaces
added 131 characters in body
May
1
comment Banach-Stone Theorem in Lipschitz-free spaces
I might be missing something but non-linearity doesn't seem to be essential here. Indeed, by the Mazur-Ulam theorem such map $T$ is affine and hence $T-T(0)I$ is a linear isometry.
Apr
21
comment Characterizations of Wiener algebra
As for (3), $C^0_{(0)}$ contains a copy of $c_0$ (take the linear span of a sequence disjointly supported functions), whereas for $L_1(\mu)$ this is clearly impossible for many reasons (e.g. because $L_1(\mu)$ is weakly sequentially complete).
Apr
17
reviewed Approve What is a simplicial commutative ring from the point of view of homotopy theory?
Mar
18
comment Images of $\{0,1\}^\kappa$
(To a now-deleted response) that cannot be right. Every subspace of $\{0,1\}^\kappa$ is zero-dimensional. As Bill says, every compact Hausdorff space is a continuous image of a zero-dimensional space and each zero-dimensional space $X$ embeds into $\{0,1\}^\kappa$ (for $\kappa$ equal to the weight of $X$). See Engelking's General topology.
Mar
18
revised Images of $\{0,1\}^\kappa$
added 44 characters in body
Mar
18
revised Images of $\{0,1\}^\kappa$
edited body
Mar
18
answered Images of $\{0,1\}^\kappa$
Mar
4
revised Communal problem books
a somewhat peculiar spelling corrected
Mar
1
revised Are countable unions of metrizable spaces metrizable too?
added 22 characters in body; edited title
Mar
1
comment The Banach space of bounded functions with countable support
arxiv.org/abs/1502.03026
Mar
1
comment What if Current Foundations of Mathematics are Inconsistent?
People were saying the same about the USSR.
Feb
26
revised Comparing cardinalities of the spectrum of two masas in $B(H)$
will add that later
Feb
26
revised Comparing cardinalities of the spectrum of two masas in $B(H)$
added 597 characters in body
Feb
26
comment Comparing cardinalities of the spectrum of two masas in $B(H)$
No, if $K$ satisfies the countable chain condition (and certainly the spectrum $K$ of $L_\infty(\mu)$ for a probability measure $\mu$ does), then no subspace of $C(K)$ is isomorphic to $c_0(\omega_1)$. (This is easy modulo certain prehistoric facts from Banach space theory.) I suggest deleting the old comments.