bounded integral operators spaces de halmos sunder (14 resultados)

1st edition. Fine copy in the original title-blocked cloth. Remains particularly well-preserved overall; tight, bright, clean and strong. Physical description; XVI, 134 pp. Notes; Includes bibliographical references and index. Contents; §1. Measure Spaces -- Example 1.1. Separable, not ?-finite -- Example 1.2. Finite, not separable -- §2. Kernels -- § 3. Domains -- Example 3.1. Domain 0 -- Example 3.2. Hilbert transform -- Problem 3.3. Closed domain -- Example 3.4. Dense domain -- Example 3.5. Dense domain -- Example 3.6. Non-closed kernel -- Example 3.7. Non-closed kernel -- Theorem 3.8. Carleman kernels -- Lemma 3.9. Dominated subsequences -- Theorem 3.10. Full domain -- Example 3.11. Everywhere defined kernels -- Problem 3.12. Closed domains and kernels -- §4. Boundedness -- Lemma 4.1. Square integrable kernels -- Example 4.2. Dyads -- Lemma 4.3. Rank 1 -- Corollary 4.4. Finite rank -- Theorem 4.5. Hilbert-Schmidt operators -- Corollary 4.6. Compactness -- Corollary 4.7. Singular values -- §5. Examples -- Example 5.1. Inflated identity -- Theorem 5.2. Schur test -- Example 5.3. Abel kernel -- Example 5.4. Cesàro kernel -- Example 5.5. Hilbert-Hankel matrix -- Theorem 5.6. Toeplitz matrices -- Example 5.7. Hilbert-Toeplitz matrix -- Example 5.8. Discrete Fourier transform -- §6. Isomorphisms -- Theorem 6.1. Induced unitary operators -- Theorem 6.2. Transforms of kernels -- Corollary 6.3. Unitary equivalence -- Corollary 6.4. Preservation of structure -- Example 6.5. Projection on L2(II) -- Example 6.6. Atomic spaces versus ? -- §7. Algebra -- Problem 7.1. Multipliability -- Example 7.2. Compact Fourier transform -- Theorem 7.3. Operators on atomic spaces -- Lemma 7.4. Integrable approximation -- Theorem 7.5. Conjugate transposes -- Corollary 7.6. Atomic domain -- Corollary 7.7. Matrices -- §8. Uniqueness -- Theorem 8.1. Uniqueness -- Problem 8.2. Determination -- Example 8.3. Non-measurable kernel -- Problem 8.4. Measurability -- Theorem 8.5. Identity operator -- Theorem 8.6. Multiplication operators -- §9. Tensors -- Theorem 9.1. Direct sums -- Corollary 9.2. Carleman kernels -- Theorem 9.3. Tensor products -- Problem 9.4. Bounded kernels -- Theorem 9.5. Tensor multiplicativity of Int -- Theorem 9.6. Tensors with dyads -- Example 9.7. Isometry on L2(II) -- Example 9.8. Inflations as tensor products -- Theorem 9.9. Bounded matrices -- Corollary 9.10. Schur products -- Example 9.11. Schur products with dyads -- §10. Absolute Boundedness -- Example 10.1. Hilbert-Toeplitz matrix -- Example 10.2. Discrete Fourier transform -- Example 10.3. Direct sum matrix -- Example 10.4. Divisible spaces -- Theorem 10.5. Characterization -- Corollary 10.6. Adjoints -- Theorem 10.7. Products -- Theorem 10.8. Non-invertibility -- Theorem 10.9. Schur products -- Example 10.10. Unbounded Schur products -- Remark 10.11. Tensor quotients -- §11. Carleman Kernels -- Example 11.1. Absolutely bounded, not Carleman -- Theorem 11.2. Inclusion relations -- Example 11.3. Counterexamples -- Theorem 11.4. Strong boundedness -- Theorem 11.5. Carleman functions -- Theorem 11.6. Right ideal -- Corollary 11.7. Non-invertibility -- Problem 11.8. Right ideal -- Theorem 11.9. Co-boundedness -- Theorem 11.10. Hermitian kernels -- Theorem 11.11. Normal Carleman adjoints -- Problem 11.12. Normal integral adjoints -- Example 11.13. Non-Carleman integral adjoint -- §12. Compactness -- Lemma 12.1. Convolution kernels on L1 -- Theorem 12.2. Convolution kernels on L2 -- Corollary 12.3. Compactness -- Example 12.4. Non-integral, compact -- §13. Compactness -- Lemma 13.1. Large characteristic functions -- Lemma 13.2. Absolute continuity -- Example 13.3. Non-absolute continuity -- Lemma 13.4. Hille-Tamarkin kernels -- Example 13.5. Non-Hille-Tamarkin kernels -- Remark 13.6. Hille-Tamarkin operators -- Lemma 13.7. Integrable kernels -- Theorem 13.8. compactness -- Corollary 13.9. Hilbert-Schmidt approximation -- § 14. Essential Spectrum -- Example 14.1. Tensor products and spectra -- Theorem 14.2. Atkinson's theorem -- Theorem 14.3. Normal operators -- Theorem 14.4. A and A*A -- Corollary 14.5. A and AA* -- Theorem 14.6. Orthonormal sequences, left -- Corollary 14.7. Orthonormal sequences, right -- Remark 14.8. Absolute boundedness and invertibility -- Remark 14.9. Non-emptiness -- Theorem 14.10. Normal Carleman operators -- Lemma 14.11. Nearly invariant subspaces -- Remark 14.12. Hilbert-Schmidt strengthening -- Theorem 14.13. Weyl-von Neumann theorem -- Problem 14.14. Normal generalization -- Problem 14.15. Quasidiagonal generalization -- §15. Characterization -- Theorem 15.1. Integral operator, essential spectrum -- Remark 15.2. Right versus left -- Corollary 15.3. Unitary transforms -- Lemma 15.4. Matrix inflations -- Remark 15.5. Partially atomic spaces -- Lemma 15.6. Perturbations of Hermitian operators -- Theorem 15.7. Carleman operator, essential spectrum -- Corollary 15.8. Carleman if and only if integral -- Example 15.9. Unilateral shift -- Example 15.10. Non-simultaneity of A and A* -- Theorem 15.11. Simultaneity of A and A* -- Corollary 15.12. Simultaneous integral representability -- Lemma 15.13. Large 0 direct summand -- Theorem 15.14. Simultaneous Carleman representability -- Corollary 15.15. Simultaneous Carleman if and only if integral -- Problem 15.16. Absolutely bounded operators -- Theorem 15.17. Essential non-invertibility of A*A+AA* -- Theorem 15.18. Absolutely bounded operators -- §16. Universality -- Theorem 16.1. Universal integral operators -- Remark 16.2. Universal Carleman operators -- Problem 16.3. Small unitary transforms -- Lemma 16.4. Operator norm -- Theorem 16.5. Universally absolutely bounded matrices -- §17. Recognition -- Remark 17.1. Pointwise domination -- Theorem 17.2. Carleman characterization -- Corollary 17.3. Hilbert-Schmidt characterization -- Problem 17.4. Integral characterization -- Theorem 17.5. Orthonormal Carleman characterization -- Problem 17.6. Orthonormal integral characterization -- Theorem 17.

1st edition. Fine copy in the original title-blocked cloth. Remains particularly well-preserved overall; tight, bright, clean and strong. Physical description; XVI, 134 pp. Notes; Includes bibliographical references and index. Contents; §1. Measure Spaces -- Example 1.1. Separable, not ?-finite -- Example 1.2. Finite, not separable -- §2. Kernels -- § 3. Domains -- Example 3.1. Domain 0 -- Example 3.2. Hilbert transform -- Problem 3.3. Closed domain -- Example 3.4. Dense domain -- Example 3.5. Dense domain -- Example 3.6. Non-closed kernel -- Example 3.7. Non-closed kernel -- Theorem 3.8. Carleman kernels -- Lemma 3.9. Dominated subsequences -- Theorem 3.10. Full domain -- Example 3.11. Everywhere defined kernels -- Problem 3.12. Closed domains and kernels -- §4. Boundedness -- Lemma 4.1. Square integrable kernels -- Example 4.2. Dyads -- Lemma 4.3. Rank 1 -- Corollary 4.4. Finite rank -- Theorem 4.5. Hilbert-Schmidt operators -- Corollary 4.6. Compactness -- Corollary 4.7. Singular values -- §5. Examples -- Example 5.1. Inflated identity -- Theorem 5.2. Schur test -- Example 5.3. Abel kernel -- Example 5.4. Cesàro kernel -- Example 5.5. Hilbert-Hankel matrix -- Theorem 5.6. Toeplitz matrices -- Example 5.7. Hilbert-Toeplitz matrix -- Example 5.8. Discrete Fourier transform -- §6. Isomorphisms -- Theorem 6.1. Induced unitary operators -- Theorem 6.2. Transforms of kernels -- Corollary 6.3. Unitary equivalence -- Corollary 6.4. Preservation of structure -- Example 6.5. Projection on L2(II) -- Example 6.6. Atomic spaces versus ? -- §7. Algebra -- Problem 7.1. Multipliability -- Example 7.2. Compact Fourier transform -- Theorem 7.3. Operators on atomic spaces -- Lemma 7.4. Integrable approximation -- Theorem 7.5. Conjugate transposes -- Corollary 7.6. Atomic domain -- Corollary 7.7. Matrices -- §8. Uniqueness -- Theorem 8.1. Uniqueness -- Problem 8.2. Determination -- Example 8.3. Non-measurable kernel -- Problem 8.4. Measurability -- Theorem 8.5. Identity operator -- Theorem 8.6. Multiplication operators -- §9. Tensors -- Theorem 9.1. Direct sums -- Corollary 9.2. Carleman kernels -- Theorem 9.3. Tensor products -- Problem 9.4. Bounded kernels -- Theorem 9.5. Tensor multiplicativity of Int -- Theorem 9.6. Tensors with dyads -- Example 9.7. Isometry on L2(II) -- Example 9.8. Inflations as tensor products -- Theorem 9.9. Bounded matrices -- Corollary 9.10. Schur products -- Example 9.11. Schur products with dyads -- §10. Absolute Boundedness -- Example 10.1. Hilbert-Toeplitz matrix -- Example 10.2. Discrete Fourier transform -- Example 10.3. Direct sum matrix -- Example 10.4. Divisible spaces -- Theorem 10.5. Characterization -- Corollary 10.6. Adjoints -- Theorem 10.7. Products -- Theorem 10.8. Non-invertibility -- Theorem 10.9. Schur products -- Example 10.10. Unbounded Schur products -- Remark 10.11. Tensor quotients -- §11. Carleman Kernels -- Example 11.1. Absolutely bounded, not Carleman -- Theorem 11.2. Inclusion relations -- Example 11.3. Counterexamples -- Theorem 11.4. Strong boundedness -- Theorem 11.5. Carleman functions -- Theorem 11.6. Right ideal -- Corollary 11.7. Non-invertibility -- Problem 11.8. Right ideal -- Theorem 11.9. Co-boundedness -- Theorem 11.10. Hermitian kernels -- Theorem 11.11. Normal Carleman adjoints -- Problem 11.12. Normal integral adjoints -- Example 11.13. Non-Carleman integral adjoint -- §12. Compactness -- Lemma 12.1. Convolution kernels on L1 -- Theorem 12.2. Convolution kernels on L2 -- Corollary 12.3. Compactness -- Example 12.4. Non-integral, compact -- §13. Compactness -- Lemma 13.1. Large characteristic functions -- Lemma 13.2. Absolute continuity -- Example 13.3. Non-absolute continuity -- Lemma 13.4. Hille-Tamarkin kernels -- Example 13.5. Non-Hille-Tamarkin kernels -- Remark 13.6. Hille-Tamarkin operators -- Lemma 13.7. Integrable kernels -- Theorem 13.8. compactness -- Corollary 13.9. Hilbert-Schmidt approximation -- § 14. Essential Spectrum -- Example 14.1. Tensor products and spectra -- Theo.

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