The fermionic second quantization operator is shown to be bounded by a power of the number operator given that the operator belongs to the von Neumann–Schatten class, . Conversely, number operator estimates for imply von Neumann–Schatten conditions on . Quadratic creation and annihilation operators are treated as well.
REFERENCES
1.
Bakić
, D.
and Guljaš
, B.
, “Which operators approximately annihilate orthonormal bases?
” Acta Sci. Math.
64
, 601
(1998
).2.
Bhagwat
, K. V.
and Subramanian
, R.
, “Inequalities between means of positive operators
,” Math. Proc. Cambridge Philos. Soc.
83
, 393
(1978
).3.
Carey
, A. L.
and Ruijsenaars
, S. N. M.
, “On fermion gauge groups, current algebras and Kac-Moody algebras
,” Acta Appl. Math.
10
, 1
(1987
).4.
Favorov
, S. Yu.
, “Zero sets of entire functions of exponential type with additional conditions on the real line
,” Algebra Anal.
20
, 138
(2008
).5.
Grosse
, H.
and Langmann
, E.
, “A superversion of quasifree second quantization. I. Charged particles
,” J. Math. Phys.
33
, 1032
(1992
).6.
Mond
, B.
and Pečarić
, J. E.
, “Remarks on Jensen’s inequality for operator convex functions
,” Ann. Univ. Mariae Curie-Skłodowska Sect. A
47
, 96
(1993
).7.
Ottesen
, J. T.
, “Infinite-dimensional groups and algebras in quantum physics
,” Lect. Notes Phys.
27
, 8
(1995
).8.
Robinson
, P. L.
, “Fermionic Gaussians
,” Math. Proc. Cambridge Philos. Soc.
118
, 543
(1995
).9.
Vasudeva
, H. L.
and Singh
Mandeep
, “Weighted power means of operators
,” Rend. Semin. Mat. Torino
66
, 131
(2008
).© 2010 American Institute of Physics.
2010
American Institute of Physics
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