Spaces of p-integrable Functions with Respect to a Vector Measure

Fernández, A.; Mayoral, Fernando; Naranjo, Francisco; Sáez, C.; Pérez, Enrique Alfonso Sánchez

doi:10.1007/s11117-005-0016-z

Cited by 66 publications

(93 citation statements)

References 25 publications

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“…The reader can find more information on these spaces in [5,6,12,13]. Two interesting facts that will be used in the paper are that the space of multiplication operators from…”

Section: Background and Notationmentioning

confidence: 99%

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Factorization Theorems for Homogeneous Maps on Banach Function Spaces and Approximation of Compact Operators

Rueda

Pérez

2014

Mediterr. J. Math.

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Rueda, P.; Sánchez Pérez, EA. (2015). Factorization theorems for homogeneous maps on banach function spaces and approximation of compact operators. Mediterranean Journal of Mathematics. 12(1):89-115. doi:10.1007/s00009-014-0384-3 0378-620X/15/010089-27. FACTORIZATION THEOREMS FOR HOMOGENEOUS MAPS ON BANACH FUNCTION SPACES AND APPROXIMATION OF COMPACT OPERATORS PILAR RUEDA AND ENRIQUE A. SÁNCHEZ-PÉREZAbstract. In this paper we characterize compact linear operators from Banach function spaces to Banach spaces by means of approximations with bounded homogeneous maps. To do so, we undertake a detailed study of such maps, proving a factorization theorem and paying special attention to the equivalent strong domination property involved. Some applications to compact maximal extensions of operators are also given. Banach function space and p-th power and compact operator and homogeneous operator. 46E30 and 47B38 and 46B42 and 46B28

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“…The reader can find more information on these spaces in [5,6,12,13]. Two interesting facts that will be used in the paper are that the space of multiplication operators from…”

Section: Background and Notationmentioning

confidence: 99%

“…For example, the following result is a direct application of Corollary 3. We need that L p (m T ) = L p w (m T ) for assuring the Fatou property for L p (m T ), what happens for instance if E is reflexive (see [5] for sufficient conditions for this to hold).…”

Section: Applications: Compact Optimal Extensions For Essentially Commentioning

confidence: 99%

Factorization Theorems for Homogeneous Maps on Banach Function Spaces and Approximation of Compact Operators

Rueda

Pérez

2014

Mediterr. J. Math.

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“…Let 1 ≤ p < ∞. The space L p (m) of p-integrable functions with respect to m (that is, equivalence classes of measurable functions f which differ on a set of null m-semivariation such that | f | p is m-integrable) is well known; it has been studied [3] Representation of the (pre)dual of L p (m) 213 in [5,11,12]. This space endowed with the almost everywhere order and with the norm given by…”

Section: I])mentioning

confidence: 99%

“…Since the m-weak topology is weaker than the weak topology of the space L p (m), the compactness property required in Theorem 3.4 is satisfied if the space L q (m) is reflexive; some results regarding reflexivity of this space may be found in [5]. In fact, from [6], it is known that the space L q (m) is reflexive if and only if its unit ball is compact for the m-weak topology.…”

Section: I])mentioning

confidence: 99%

TENSOR PRODUCT REPRESENTATION OF THE (PRE)DUAL OF THE L^p-SPACE OF A VECTOR MEASURE

Ferrando¹,

Pérez²

2009

J. Aust. Math. Soc.

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The duality properties of the integration map associated with a vector measure m are used to obtain a representation of the (pre)dual space of the space L p (m) of p-integrable functions (where 1 < p < ∞) with respect to the measure m. For this, we provide suitable topologies for the tensor product of the space of q-integrable functions with respect to m (where p and q are conjugate real numbers) and the dual of the Banach space where m takes its values. Our main result asserts that under the assumption of compactness of the unit ball with respect to a particular topology, the space L p (m) can be written as the dual of a suitable normed space.2000 Mathematics subject classification: primary 46G10; secondary 46B28.

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“…For the basic properties of this space, we refer the reader to [5] and [10,Chapter 3]. The mapping I :…”

Section: Introductionmentioning

confidence: 99%

Interpolation subspaces of 𝐿¹ of a vector measure and norm inequalities for the integration operator

Rodríguez¹,

Rodríguez²,

Pérez³

2012

Contemporary Mathematics

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Spaces of p-integrable Functions with Respect to a Vector Measure

Cited by 66 publications

References 25 publications

Factorization Theorems for Homogeneous Maps on Banach Function Spaces and Approximation of Compact Operators

Factorization Theorems for Homogeneous Maps on Banach Function Spaces and Approximation of Compact Operators

TENSOR PRODUCT REPRESENTATION OF THE (PRE)DUAL OF THE L^p-SPACE OF A VECTOR MEASURE

Interpolation subspaces of 𝐿¹ of a vector measure and norm inequalities for the integration operator

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Spaces of p-integrable Functions with Respect to a Vector Measure

Cited by 66 publications

References 25 publications

Factorization Theorems for Homogeneous Maps on Banach Function Spaces and Approximation of Compact Operators

Factorization Theorems for Homogeneous Maps on Banach Function Spaces and Approximation of Compact Operators

TENSOR PRODUCT REPRESENTATION OF THE (PRE)DUAL OF THE Lp-SPACE OF A VECTOR MEASURE

Interpolation subspaces of 𝐿¹ of a vector measure and norm inequalities for the integration operator

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Product

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TENSOR PRODUCT REPRESENTATION OF THE (PRE)DUAL OF THE L^p-SPACE OF A VECTOR MEASURE