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diagram of LCTVS properties
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LCTVS
cluster_key_col1
cluster_key_col2
cluster_key_col3
FD
FD
Hi
Hi
FD>Hi
NuFr
FD>NuFr
IP
IP
Hi>IP
ReBa
Hi>ReBa
Nu
Nu
Sc
Sc
Nu>Sc
Ba
Ba
Fr
Fr
Ba>Fr
No
No
Ba>No
LB
LB
Ba>LB
IP>No
Mo
Mo
Re
Re
Mo>Re
UB
UB
Bo
Bo
UB>Bo
QCQB
UB>QCQB
LF
LF
Fr>LF
Me
Me
Fr>Me
Pt
Pt
Fr>Pt
DF
DF
No>DF
No>Me
QB
QB
Bo>QB
LF>UB
LB>DF
LB>LF
Me>Bo
NuFr>Nu
NuFr>Mo
ReFr
NuFr>ReFr
LC
LC
QC
QC
Sq
Sq
QC>Sq
BC
BC
Pt>BC
Cp
Cp
BC>Cp
Sq>LC
Cp>QC
Bl
Bl
Re>Bl
MkSR
Re>MkSR
SR
SR
SR>QC
Mk
Mk
QB>Mk
Bl>QB
MkSR>SR
MkSR>Mk
QCQB>QC
QCQB>Bl
ReBa>Ba
ReBa>ReFr
ReFr>Fr
ReFr>Re
yFD
yHi
xFD
FD: FiniteDimensional
yDF
Key to symbols
yNo
xDF
DF: DF
yPt
yBC
xPt
Pt: Ptak Space
yNu
xHi
Hi: Hilbert (technically, admits a Hilbertian structure)
yBa
xNu
Nu: Nuclear
yIP
xBa
Ba: Banach (technically, complete and normable)
yMo
xIP
IP: Topology from an innerproduct
ySc
xMo
Mo: Montel
yUB
xSc
Sc: Schwartz
yFr
xUB
UB: Ultrabornological
yZ1
xFr
Fr: Fréchet
yBo
xNo
No: Normable space
yLF
xBo
Bo: Bornological
yLB
xLF
LF: strict inductive sequence of Fréchet spaces
yMe
xLB
LB: strict inductive sequence of Banach spaces
yLC
xMe
Me: Metrisable
yQC
xLC
LC: Locally Complete
yZ2
xQC
QC: QuasiComplete
ySq
xBC
BC: Br Space
yCp
xSq
Sq: Sequentially Complete
yRe
xCp
Cp: Complete
ySR
xRe
Re: Reflexive
yQB
xSR
SR: SemiReflexive
yMk
xQB
QB: QuasiBarrelled
yBl
xMk
Mk: Mackey
yZ3
xBl
Bl: Barrelled
category:
svg
Revised on October 28, 2010 08:31:07 by
Toby Bartels
(75.88.77.52)
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Source
 Linked from:
von Neumann algebra
,
Banach space
,
Hilbert space
,
topological vector space
,
operator algebra
,
functional analysis
,
locally convex space
,
distribution
,
von Neumann algebra factor
,
Fredholm operator
,
reflexive Banach space
,
heat kernel
,
Sobolev space
,
Lebesgue space
,
bounded operator
,
unbounded operator
,
bornological topological vector space
,
barreled topological vector space
,
functional analysis  contents
,
functional analysis bibliography
,
second lctvs diagram dot source
,
state on an operator algebra
,
SVG images
,
projective Banach space
,
integral transform
,
Hilbert module
,
Gelfand triple
,
Kuiper's theorem
,
selfadjoint operator
,
KKtheory
,
Etheory
,
Riesz representation theorem
,
index
,
functional calculus
,
Gelfand duality
,
contents of contents
,
selfadjoint extension
,
AlfsenShultz theorem
,
canonical Hilbert space of halfdensities
,
bounded set
,
Spin^c Dirac operator
,
sequence space
,
MishchenkoFomenko index theorem
,
Banach coalgebra
,
Hilbert bimodule
,
stereotype space
,
continuous multilinear operator
,
precompact space
,
convergence vector space
,
continuously differentiable map
,
Schwartz space
,
absolutely convex subset
,
absorbing subset
,
nuclear space
,
circled set
,
square integrable function
,
enveloping von Neumann algebra
 Included from:
locally convex space