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47:
can be expressed using operators that are pseudo-monotone, and pseudo-monotonicity in turn implies the existence of solutions to these problems.
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381:{\displaystyle \liminf _{j\to \infty }\langle T(u_{j}),u_{j}-v\rangle \geq \langle T(u),u-v\rangle .}
870:
808:
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762:
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476:. Texts in Applied Mathematics 13 (Second ed.). New York: Springer-Verlag. p. 367.
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254:{\displaystyle \limsup _{j\to \infty }\langle T(u_{j}),u_{j}-u\rangle \leq 0,}
146:{\displaystyle u_{j}\rightharpoonup u{\mbox{ in }}X{\mbox{ as }}j\to \infty }
495:
128:
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59:, || ||) be a reflexive Banach space. A map
281:
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100:
914:
838:
817:
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851:Spectral theory of ordinary differential equations
380:
253:
145:
474:An introduction to partial differential equations
472:Renardy, Michael & Rogers, Robert C. (2004).
283:
183:
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91:(not necessarily continuous) and if whenever
8:
372:
345:
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198:
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411:, reflexive Banach space and suppose that
396:Using a very similar proof to that of the
327:
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186:
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127:
117:
105:
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35:is one that is, in some sense, almost as
804:Group algebra of a locally compact group
392:Properties of pseudo-monotone operators
7:
431:and pseudo-monotone. Then, for each
293:
193:
140:
14:
960:
959:
886:Topological quantum field theory
488:(Definition 9.56, Theorem 9.57)
75:into its continuous dual space
400:, one can show the following:
357:
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317:
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1:
682:Uniform boundedness principle
433:continuous linear functional
1012:
825:Invariant subspace problem
442:, there exists a solution
955:
545:
264:it follows that, for all
794:Spectrum of a C*-algebra
407:, || ||) be a
22:pseudo-monotone operator
891:Noncommutative geometry
43:. Many problems in the
991:Calculus of variations
947:Tomita–Takesaki theory
922:Approximation property
866:Calculus of variations
382:
255:
147:
45:calculus of variations
942:Banach–Mazur distance
905:Generalized functions
398:Browder–Minty theorem
383:
256:
148:
33:continuous dual space
687:Kakutani fixed-point
672:Riesz representation
279:
179:
98:
871:Functional calculus
830:Mahler's conjecture
809:Von Neumann algebra
523:Functional analysis
446: ∈
438: ∈
419: →
268: ∈
67: →
896:Riemann hypothesis
595:Topological vector
378:
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132:
122:
973:
972:
876:Integral operator
653:
652:
282:
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121:
41:monotone operator
1003:
963:
962:
881:Jones polynomial
799:Operator algebra
543:
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450:of the equation
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166:converges weakly
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89:bounded operator
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1005:
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1002:
1001:
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996:Operator theory
976:
975:
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915:Advanced topics
910:
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738:Hilbert–Schmidt
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702:Gelfand–Naimark
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81:pseudo-monotone
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932:Choquet theory
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784:Banach algebra
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707:Banach–Alaoglu
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635:Locally convex
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79:is said to be
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986:Banach spaces
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937:Weak topology
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861:Index theorem
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818:Open problems
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483:0-387-00444-0
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927:Balanced set
901:Distribution
839:Applications
692:Krein–Milman
677:Closed graph
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37:well-behaved
29:Banach space
21:
15:
856:Heat kernel
846:Hardy space
753:Trace class
667:Hahn–Banach
629:Topological
18:mathematics
980:Categories
789:C*-algebra
604:Properties
466:References
51:Definition
763:Unbounded
758:Transpose
716:Operators
645:Separable
640:Reflexive
625:Algebraic
611:Barrelled
373:⟩
367:−
346:⟨
343:≥
340:⟩
334:−
299:⟨
294:∞
291:→
243:≤
240:⟩
234:−
199:⟨
194:∞
191:→
141:∞
138:→
112:⇀
31:into its
26:reflexive
965:Category
777:Algebras
659:Theorems
616:Complete
585:Schwartz
531:glossary
429:coercive
768:Unitary
748:Nuclear
733:Compact
728:Bounded
723:Adjoint
697:Min–max
590:Sobolev
575:Nuclear
565:Hilbert
560:Fréchet
525: (
425:bounded
24:from a
743:Normal
580:Orlicz
570:Hölder
550:Banach
539:Spaces
527:topics
480:
172:) and
156:(i.e.
555:Besov
403:Let (
87:is a
71:from
55:Let (
39:as a
903:(or
621:Dual
478:ISBN
409:real
20:, a
423:is
168:to
83:if
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